I applied for my uk state pension in July last year. It couldn't be done on-line.
I downloaded all the paperwork - extensive form. Also they what to know all my employment history and where I have lived since birth!!! Thankfully I had an old C.V. so it was easy(ish) to do but if you have moved around alot it is a bit difficult to remember your home addresses.
That said all original document were returned quickly and I got notification of payments to my account a few weeks AFTER it had been paid but I think this was due to postage delays more than anything else.