£600 or so would not be unreasonable as a budget.
Several options spring to mind.
If you want interchangeable lenses then M4/3 with the 45mm f1.8 could be a good option. There are various small bodies around, but if you like something to grip hold of then the EM1 used can be found for a relative steal. Then there's the Sony A6xxx series, pair that with a 50mm prime and you have something that would be good for project shots and portraiture alike. It will probably me more flexible as the 45mm f1.8 on m4/3 is 90mm eq which makes it a bit more difficult for small spaces.
If you want fixed focal length I doubt you'd get FF as the RX1's are still pretty pricey used (£899 for a good condition). A good option would be one of the Fuji X100 series. A lot of people still like the original one as it has the bayer sensor and not prone to Fuji artefacts. Also, a lot of folk say it has one of the best film like qualities of all digital cameras, but how much of this is the camera and how much is down to Fuji presets I don't know. The nice thing with the X100's is that you can add adapters to make it wide angle (28mm), or more tele (50mm eq), albeit at quite a cost.
Another option would be the Panny LX100, more or less an m4/3 but with a fixed lens which is relatively fast (f2.8 at the long end).
The last option I'll suggest for fixed focal length would be the Ricoh GR but this is wide angle and not really ideal for portraits.
The X100 is a good suggestion, it's not just a lot cheaper than the RX1 but the lens is tiny in comparison as well which makes it easier to carry. 35mm equivalent is a lot shorter than the more portrait FL a 50mm on APS-C gives but I find it's quite a versatile one, I went with the RX1 this year and surprised how much use I get out of it.
FWIW on M4/3rds the 45mm F1.8 Olympus is very long for indoor food photography (90mm FF equivalent field of view).
You might be a bit self conscious standing over the next table to snap your starter data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7
Again the 45mm field of view makes snapping someone over the table in the average restaurant pretty close up.
In good to reasonable light the 14-42mm EZ Olympus lens is capable and cheap.
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Sashimi Bowl by AMc UK, on Flickr
The Olympus 17mm f1.8 is very good, you get a lot in the frame (34mm eq).Obviously for headshots it's not quite as handy but I use my for family portraits when we're out and about.
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Sushi platter by AMc UK, on Flickr
The Panasonic 25mm F1.7 is cheap and very capable.This was taken in terrible light.
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Cosmopolitan and Dirty Martini by AMc UK, on Flickr
The Olympus 45mm f1.8 is obviously the greatest for bokeh.
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Bulls in a China Shot by AMc UK, on Flickr
One advantage of food is it tends not to move much data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7, given you're likely to be sitting down too then you can use a stabilised body or lens or combination to drop the shutter speed quite low.All the more recent Olympus bodies are stabilised.Some of the Panasonic ones are too, but I don't know their range.
If you were looking for an EVF then the Olympus E-M10ii is a great balance of size, 5 axis stabilisation and compactness.
If you don't mind about an EVF then the PEN range is more compact.The E-PL8 or E-PL9 will both be a good bet esp. used.The E-P5 is an older model basically the former top of the line E-M1 Mki without a viewfinder - a used bargain and very capable with a small prime or the EZ zoom.
Finally if the budget would stretch to it then the PEN-F is a beautiful camera which includes an EVF and the later 20MP sensor etc.
I put my shots in albums by body and lens so you can see what I've done with the 3 lenses I've suggested and my E-M10 Mkii
Olympus 14-42mm f3.5-5.6 EZ Pancake
Olympus M.14-42mm F3.5-5.6 EZ Pancake
Olympus 17mm f1.8
Olympus f1.8 17mm
Panasonic 25mm f1.7
Panasonic f1.7 25mm (LUMIX G 25/F1.7)
Olympus 45mm f1.8
Olympus f1.8 45mm
Olympus OM-D E-M10 Mkii
Olympus OM-D E-M10 Mkii
Given you've got another full size camera, I'd probably look at one of the PEN bodies and couple it with either the Panasonic 25mm f1.7 or if you don't mind used the Olympus 17mm f1.8.
The 17mm f1.8 is indeed a very nice lens, giving pretty much the 'classic' 35mm FOV (34mm for those pedantic ones data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7). It does render nicely, but the only issue is if you want blurred backgrounds it's not as easy to achieve with a 34mm f3.5 in FF terms. It's unclear whether the OP actually means Bokeh or shallow depth of field though. IMO the bokeh from the 17m f1.8 is very pleasing.
The 14-42mm is a nice lens, but wouldn't be my lens of choice for low light data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7
Agreed - which is why I have the 17, 25 and 45mm data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7
Thing is it can do a bit more than the raw specs suggest if it's held steady on a stabilised body.You're never going to get the slim depth of field as a prime or a larger sensor system.
If you were prepared to compromise on price and size then there's the 12-40 f2.8 Olympus PRO but I've never felt this fitted my "small and light" choice. data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7
Nice food AMc - but they show the snag with modern cameras - the inability to move the plane of focus.
OP has suggested £600 Budget which should be enough !.... but the term "Compact" is rather difficult to resolve - particularly as compacts are for "general use" and shallow DoF is unlikely to endear the Public. I wonder that you can't find a canon mirrorless that has a slightly smaller body and would be less obtrusive? BUT I wonder that no-one will notice - and then there is the issue of good lighting - not easy to fix that when there are diners about....
Of course you might save some money if yr existing Canon lens can be adapted . . . but it's probably "too big" to go unnoticed.
Another tack:- come clean with the Restaurant ( having yr Portfolio should help ), and allow you to take the food home.This might reduce the number of Restaurants.... but means good pictures should be easier to achieve. You might be a discount off the Bill.
Good luck.
Seriously? You can have the plane of focus wherever you choose.
There are plenty of high end compact cameras geared towards the serious photographer
From my experience the public like shallow DOF and associate it with the ‘pro look’. In fact it’s so popular the latest phones are trying to replicate it, although software based rather than true shallow DOF.
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If you ignore the budget, it sounds like you want a Sony RX1RII data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7
Link, in case you're curious; Sony RX1R II Professional Compact Camera with 35mm Sensor
More seriously, the earlier suggestion of an A6000 50 f/1.8 OSS is a good one, you could instead opt for the 35 f/.18 OSS if you wanted a wider lens (but would stretch your budget a bit).
Genuinely baffled by this comment. There is no “snag”.
The shallow depth of focus is intentional in all those shots to emphasise the subject and isolate from the background. I could have stopped down for more depth of focus but why would I?
As @snerkler says the broader non photographer audience associates this look with “professional pictures”.
Mobile manufacturers are jumping through hoops, adding second cameras to replicate the effect or software processing to fake it.
Blurred background and Bokeh are often used interchangeably I struggle to see that anyone would be looking to spend £600 to get crisp focus from 1cm to infinity when any old compact or phone can make a stab at it.