Where can I cash a paycheck in London, if I don't have a bank account. Cheap and fast.
One of my friends had a similar issue when started working in the UK. He got a cheque, but didn't have a bank account to cash it into. Banks will only let you cash in cheques into your own account, and high street money lenders will only cash in cheques if you have a valid proof of address, and will also cut you out of at least 5% of the cheque amount.
If you have valid proof of address, then your best bet is to open a bank account. Smaller branches of banks outside of Zone 1/2 usually open your account on the spot, where you can also immediately cash your cheque, and get the full amount back. You can also later tell your employer to pay your salary to your account instead of giving it as cheques.
If you don't have a valid proof of address, you can try going to money shops, but without a proof of address they will refuse your request, or increase the amount they will keep. At one of the shops we tried to cash the cheque they told us, that they would take away 30% of the value.
If you have a job (which you ought to have, as you got a paycheck), then you should ask your employer to write you a letter, that is usually accepted by branches as a proof of address. You should try multiple branches in your area, some of them will accept your proof of address, and will open the account on the spot (which is both fast and cheap). Heck, some banks even give you some free credit. You can read more about opening a bank account without a proof of address here.