500 quid is good for you if you can get it.
A builder can do that easily .. Just make sure there are some dust sheets available, as some soot may fall. The opening will have the enamel flue pass through, then it will be open . into the chimney entry .. or, if you have a liner it will be attached to that and unplug. You should have a piece of fibre-board or blanking material to close the opening off .. or plug the liner. The chimney top should have a vented cowl in metal or terracotta fitted if you no longer plan to use the chimney.
Straight enamel flues are 1M lengths normally .. It could have been shortened. Flue sizes vary, so I would give them the outlet and first part of flue at least. It's held in by not much more than fire cement at joints, and maybe a steady bracket inside the register plate in the opening.
Al.