I suspect that they "bumped" you to accommodate the huge backlog of people stuck at LHR. However, to avoid compensating you, they have lied and said the flight was cancelled. You should persist and demand your fees back and consequential damages. You may also wish to consider using EUCLAIMS.CO.UK. This is a Dutch based specialist company which will sue them for you on a no-win, no fee basis. You will have to pay some of your compensation to them if you win, but they have a good reputation for doing solid research into what really happened and using it to good effect in court. Good luck.
(You can instead file a claim yourself in UK court at
www.moneyclaim.gov.uk which is an online small claims court). However, the burden of proof as to what happened is on you.