I don't think most people would find the social side of UK school poor at all, tbh.
I think the single biggest difference between UK and Gm schools is the difference in remit. Gm schools are there to deliver the curriculum, and evaluate whether children have taken on board the material delivered. If they don't make the grade, they drop back a year until they do. The academic side is all -- they are not really interested in pupils' personal development, happiness or social interactions.
UK primary schools are generally pretty rigid about grouping children purely on age -- there's virtually no scope for kids to be advanced or held back, and people do occasionally moan about the inflexibility of that, particularly if they have children with late summer birthdays. However, the flip side of that is that schools are much more geared up to working with individual children wherever they may be at, and the concept of a 'Klassenziel' doesn't exist. At best this results in much more individualised and differentiated learning, though the introduction of SATS does mean that some of the most able children are left to coast while the school tries to get the borderline people up to scratch.
The schools also see themselves as having a much wider remit in terms of children's overall development, so the level of pastoral care is on the whole much more evolved than German, where it's pretty non-existent. They also IME tend to be more flexible -- I remember receiving a 5 for a piece of artwork once on the basis that I'd painted the cat purple and its tail was too thin. Wtf? Whereas ds made a model chair last year which was somehow shaped like a crocodile. It looked fab, but had the downside that you couldn't actually sit on it because the crocodile's teeth were in the way. In Gm I suspect that would have been a deal-breaker and resulted in a 4; here his teacher got him to take it round all the other classes and to the deputy head to show it off because it was so imaginative. And this isn't a particularly arty, creative school by any means. There will be huge ability/level variations in most UK primary school classrooms, which can unnerve Gms a bit, particularly the inclusion of kids who would undoubtedly be in special schools in Gm. But if it's dealt with well it really doesn't cause problems ime. Obviously there will be schools where it won't be as well-handled, but that will be true anywhere.
At secondary level, most UK schools are much stricter than Gm schools would feel able to be regarding clothing and behaviour. Gms don't always see this as a good thing ('verschult' seems to be a common phrase used) but the number of educated upper-income Germans putting their kids into UK boarding schools for some or all of their Oberstufe suggests that there's a great deal of perceived dissatisfaction with the German system (which is also what I hear anecdotally). Lack of rigour in teaching and curriculum and poor discipline seem to be the main gripes, though obviously there are UK schools of which that would be true. But there is much more variability in ethos and atmosphere across schools in UK than in Gm because they have much more organisational autonomy (national curriculum notwithstanding).
I think the class thing is much less a feature of schools (IME) than you would think, though obviously it depends on the schools. If you find a good mixed primary school in a socially mixed area that isn't top-heavy with private provision, you should be fine. Ditto out-of-school activities -- most primary schools offer a range of sports, music, art etc clubs, although availability can sometimes fluctuate. Ds has done cricket, football, multisports, Latin, Detective club (!) and drama over the past couple of years. If you want to take particular activities more seriously there are loads of non-school based organisations for sports, music, drama, etc. Obviously you can't compare eg. Berlin with Little-Puddleton-in-the-Marsh, but unless you are planning to move 15 miles from the nearest main road there will always be activities to go to, and if you're in eg. London, Oxford, Cambridge, Sheffield, Brighton etc you'll be overwhelmed with choice.
Sorry, this is an essay! Hth a bit, though. Maybe you should set aside a couple of weeks to stay in the UK and actually do some school visits? I think on the whole most parents in the UK are pleased with their child's education assuming they've been allocated a school that they've actually chosen. There are grumbles, but they tend to be localised and over specific issues. The rumblings I hear from Gm parents tend to go a bit deeper.