Drafting

cutting out the Park Lane/Shaftesbury loop in getting to the British Museum was worth it to ride down Oxford Street the whole way

jayloo, there are plenty of good routes parallel to the Roman road that mean you have to do neither--you just have to learn the lie of the land a bit. Do you have the Central London Cycle Guide published by TfL? That'll show you a lot of easier and quicker routes through this area, e.g. Marble Arch to the British Museum. Park Lane-Piccadilly-Shaftesbury Avenue is a massive detour.