Accountants ARE helpful.

As Peter my accountant said to me (before he went on holiday). I could claim my bike as capital allowance AND get 20p a mile for every journey I make for work. As we have seven sites, soon to be nine and I work from home as well sometimes that is a lot of miles a week.
Of course I have to check out the competition at nights as well, as part of my job. So quite a lot of my evening social journeys could be classified as a work journey. (Just no house parties.)
I believe that you can also get some kind of meal allowance as "fuel". Although this would be pretty pointless for me as we have a superb "staff canteen".
He is away on holiday at the moment though so I haven't actually sorted any of this out. But will let you know what comes of it.

You can't claim the 20p and the capital allowances. Claiming capital allowances means that the bike is owned by the business, which clearly isn't compatible with the 20p per mile concessionary wear and tear allowance that you can receive from your employer without it being considered a benefit in kind.

The actual tax saving on that 20p is - at most - 41%, so 8.2p.

And Object, if you got 40p per mile off of your work you have to pay tax on the extra 20p (which will be reported on your P11D).

Finally, as for the multiple sites if depends on if they are "regular" work places. If you go there a lot, it's commuting and not a "work journey", so no 20p per mile tax free!