Given the problems with debt in the UK economy, I don't understand how the government has the cash to buy up gilts, for it's quantitative easing programme? How is the UK govt. generating the cash to do this? I am guessing it is either selling some assets for cash or issuing more debt somehow?

No, it is literally just printing more money and then buying its own debt with it!

Do you think that QE is working? And will this not have any inflationary effect in long term?

I think it's not showing any significant impact, and the inflationary pressures it's creating will come back and bite us hard within the next few years.