Depends on Airport
From what I have seen it seems to depend on which airport you are flying from. At Luton they certainly enforce the one bag policy, so had to stuff handbag into suitcase and take it out again after I had got through. Crazy.
At Pisa (earlier this week) was worried as bag fuller for return (isnt it always) so unable to stuff handbag into case. Boldly went through with two bags, and handbag had the liquids in see through bag. So many items bag would not close and when I read the notices said maximum 11 items - and I had 13. However the screening staff took absolutely no notice of me at all.
Seems that the policy of one bag is not universal, and if you can then add extra bags bought airside it all seems a bit senseless.