Yes, you can attend a German university with A-Levels, I know this because I have done so myself! In fact, over the years I've been registered at 3 universities here in Germany. For 2 of them there were no minimum grades required, and for those it was enough to show my A-Level certificate (ie I had shown that I had at least the 'minimum' entrance requirement for a university.) But for one programme there were very strict admittance criteria under the Numerus Clausus process. For that I had to get my A-Levels assessed and 'converted' into German Abitur grades. There will be a body in each Bundesland responsible for doing this, and you have a pay a fairly small fee for the process (I think I paid 45 DM 20 years ago). They want to see your O-Levels AND A-Levels because a German Abitur has 10 subjects, including a mixture of arts and sciences, while A-Levels obviously have fewer and are more specialised. Because I hadn't done Maths after O-Level I was only allowed to study arts subjects, for example. I got an AAB at A-Level and this equated to a 1.3 at Abitur, which is pretty good and easily got me in to my programme of choice. So because A-Levels are more specialised they allow you to focus on your strengths and drop your weak subjects, so it's actually easier to get a good converted Abitur grade than it would be in Germany.
I don't know how they do the conversion though if you're German and have only done A-Levels without GCSEs, ie I don't know how they take into account that you haven't done the required subjects after 16. Germany doesn't have a GCSE equivalent, you just pass Year 10 and that allows you to start your Abitur.
Is that in any way clear?
A friend's daughter is considering Leipzig Uni at the moment and went to visit a few weeks ago, she said it was lovely and they're clearly keen to attract good students. There will be an international office which can answer conversion questions.
"German universities are poorly funded, they don't have the library/computer facilities and they don't have the different 'societies' that english universities have."
That varies considerably. Some programmes have excellent facilities which put the UK to shame (think of Fachhochschulen in the Neue Bundesländer), while others are cramming 400 students into a hall designed for half as many. It's true that German students tend to be older and more mature when they start, and that students are less 'nannied'.