How much U.S. currency am I allowed to carry from the U.S. to the UK? Also how many British Pounds, am I allowed to carry with me?
Collating answers from comments:
Leaving the US: You can carry as much currency as you want, but if the total value of your cash is over USD 10,000 then you must report it to US authorities.
Since departing travelers do not go through systematic customs screening, it is your own responsibility to seek out the right authorities to declare the currency to at the airport. If in doubt, ask at the check-in desk where to find Customs.
Entering the UK: You can carry as much as you want, but currency of any denomination and in aggregate amounting to more than EUR 10,000 must be declared when entering the UK. It is an EU regulation. It includes banker's drafts and travellers cheques also.
Choose the "goods to declare" lane when exiting the baggage claim hall.
In both countries authorities have surprisingly broad powers to seize large amounts of cash that they think are proceeds of crime -- so it you're even close to the 10K declaration limit you should travel with the best documentation for where the money comes from and what you're going to use it for that you can lay your hand on.
There is no limit on the amount of currency or equivalents you can carry between the US and the UK.
Related, if the total is over 10,000 local, you just have to declare it to local Customs in and out.