We had one done about 2 years ago.
Cost was approx £150 which left the stump in the ground and the cuttings 'where they fell' - would have been an extra £50 to remove debris.
Also, better to check with Local Authority that there isn't a Tree Preservation Order on it and permission is obtained. I think there's quite a hefty fine (£1000?) if you cut one down with a TPO on it.
gollob, it would be best to get at least 2 quotations. Can anyone you trust recommend a good tree surgeon? Lots of points to consider e.g. is tree surgeon certified and fully insured, will they need to use a cherry picker, any neighbour issues, any access problems, will the stump be left or ground out, will they remove the fallen tree and branches? That is just for starters.
A few years ago I used the local tree feller ( not 3 Irishmen ) to take out a 40 plus years old Rowan, They arrived on the agreed day, it was chucking it down, cut down the tree and just left a stump which was coated with some type of chemical. 6 months later they came back to grind the stump. Cost £120 to cut down tree plus £40 to grind stump , no mess on either visit, I was more than pleased. Suggest you shop around locally as some are good whilst others are not , word of mouth is also good.
I would say at least £200 to chop down and clear up, especially if the tree needs to be dismantled bit by bit and to avoid damage to nearby property. If the trunk is wide they may also need to get specialist cutters into the garden- some gardens don't have access for such machinery if it's just a narrow path.
And yes you need to check with the council
Well I don't think we were diddled but we paid £750 but that was for a huge eucalyptus, quite a bit higher than the house. It took 3 men who all had to be roped up as they took it down log by log from the top as there was nowhere for it to fall. Took everything away but left a stump that they treated.