Hello,
When I lived in Cambridge, I obtained a tourist visa to Ukraine from the Ukrainian Embassy in London. (I am a US citizen.) The process was fairly smooth, although it took a few days longer and a few pounds more than what was promised by the Embassy. I suppose it also helped that I spoke Russian, although the visa section people seemed pretty competent in English.
Of course Ukraine and Russia are different countries but not too different... same old Soviet bureaucracies. I would definitely suggest trying to do things yourself and to allow plenty of time for processing.
I read somewhere that using an alternate consulate (i.e., Edinburgh instead of London) might be better as they have fewer inquiries and are therefore a bit more efficient and nice.
Alex