That's what was happening to mine. Yes, it was really easy.
I bought the 'package' from Aga DIY Service. It costs a one-off £40 and includes a step by step guide with pics, help at the end of a phone, a new set of wicks and a 3mm drill.
I followed the instructions fine til I got to the fuel supply pipe and it was solid. So then I wondered if in fact it had a very small fuel hole and that I was trying to push something too big through it. So I phoned, at 6pm on a Fri eve, got to speak to a very nice man who said no, the fuel pipe is the same diameter all through, it gets very coked up at the end and to drill it out. So I did.
It lit first time and is burning happily as I drink my well-earned glass of wine

I was very grateful to be able to check out that one issue immediately and of course, I can do it the next time with the instructions for reminders and just the cost of a new wick.