I live in the UK in the northeast of the country.

So, when you say 'remove the bud' is that part the bit that flares out right below the stamen in the bottom pics? I understand what you are saying. I am sure I am doing OK as I am doing as you say. So long as I remove the bit in the pic and then the two sets of leaves from the top I will be fine.

Yes that is right, you can prune hard and it does not matter where as they bud back very easily.