The HMRC rate is 20p a mile, but you have to meet certain criteria- eg you can't b travelling to the same place- you have to sign something about your true base.
If you are with an umbrella company I assume you are also paying the Employer's National insurance as well as your own. Claimimg some cycling expenses at the agreed HMRC rate would reduce your liability for both NIs and reduce your tax, but it wouldn't be paid to you on top of your salary.
So if you do 100 miles a week you can claim £20 a week. Umbrella companies often then reduce your pay by £20 (subject to mimimum wage constraints). You then pay slightly less tax, NI and Employers NI on that- so maybe £9. The UC then gives you the £20 back. Overall you are £9 better off. Unless there is an admin charge.
It's an area where you need to be careful. HMRC are now coming back to umbrella companies about avoidance (currently just limited types of cases) and pursuing the employees going back 10 years or so.
I got out of UCs when i realised the main beneficiaries were the agencies and UCs