Adding a downstairs toilet in cloakroom

It sounds like space (or lack of it) is your main issue here. That being the case you may benefit from using a macerator to connect your WC to the waste stack as this allows you to connect to the main soil stack using a smaller (less obtrusive) bore of pipe. There are space saving WC units available on the market with the wash basin built into the top directly above the WC but I don't know if a macerator would fit in one so you would have to check that first. If you opt for this then make sure you get it installed by someone qualified who knows what they're doing.