I hammock pretty often now, but just rock it with a hammock and tarp, never tried one with an integral rain cover.
This guy on youtube is well known in the hammock community and does some great reviews, and also gives a good intro to hammocking:
https://www.youtube.com/user/shugemery
General thoughts are that hammock + tarp should be better as the combo provides flexibility, and is still pretty cheap. Lot’s of people have different preferences with tarp layouts – an integrated one may not give you that option.
In addition, colder months you need to insulate the underside – typically done with an underblanket – again, I’m not sure whether an integrated design would hinder that.
One more thing – consider the length of the hammock, if you’re tall you probably want a longer length hammock for comfort (and then also a larger tarp to add the weather protection).
The most common hammocks in the UK are probably DD and TenthWonder (still fairly cheap, lots of size / material options, and all pretty robust).
http://www.ddhammocks.com/
http://www.twhammocks.co.uk/