Definitely get rid of them. They serve no useful purpose at all today.
BoE inflation calculator:
Inflation calculator
According to that, 1p is worth approx. 35% less than 0.5p was worth when (1984) the halfpenny coin was withdrawn.
The ancient among you may remember all sorts of ditched coins including the toothbreaker, the two and half pence piece with a face value of six pence.