The white harness clips mean that the seat is probably made by a company called team Tex who make generic seats for different companies that all put their own covers on the seats and sell them under different names. That's why people warn about this harness style because it's an easy way to recognise that the seat is generic.
Generic seats tend to be built for cost rather than safety. You want to look at brands which build their own seats as they have more of a focus on safety. Joie as mentioned previously and Graco are good budget options. I've also found some of the cosy n safe and babyauto seats to be good budget options.
However it's a bit out of date because there are other generic brands that are not using that harness style now.
The story behind the 40mph claim is a bit less black and white - the crash test to legally sell a car seat is done at 30mph and in 2012 there was one team Tex seat with that harness style which was crash tested by the company that supplies Which? with their crash test results, this crash test is done to the NCAP conditions and is at 40mph. Generic seats, of which many have been team Tex, because they were the leading provider of generic seats in Europe for a long time, have been known to get worse scores in this test. The seat that was tested in 2012 broke and the harness detached from the seat. That model was recalled, although they do still sell a very similar looking one. I don't know if they changed the design. You'd hope so, but it's not unknown for a company not to do that. Technically it's perfectly legal because it does not fail in the test for the legal approval.
But that doesn't mean that all team Tex seats will necessarily fail at higher speeds, that's not really how it works.
If you're on a tight budget the best thing you can do is keep your baby rear facing for as long as possible. Joie and Graco have some good seats that will let you rear face to 18kg. The reason for this is that it doesn't matter how basic the seat is, rear facing is very protective and you can get good protection without spending a lot. However these seats tend not to do as well when used forward facing.
I would probably recommend the Joie steadi, or if you can keep using your seat as long as possible (at least 15 months) and you're definitely sure you don't want to rear face, maxi Cosi Tobi is the best performing belt fitted one.
You may also want to look into impact shield type seats. I found those useful when I didn't have my own car because they are easier to fit quickly. However please be aware despite better safety scores in tests, they don't actually offer any better safety than a standard forward facing seat, because they have higher incidence of other kinds of injury that aren't tested for in those tests.
Rear facing for as long as possible is the safest option without spending much money. But I agree that a £100 budget would be better if you can stretch to it at all. Some of the very cheap seats really are very flimsy. Another option is to ask around friends and family if they have a stage 2 seat they have finished using, although bear the same advice in mind about brands and rear facing. It's not advised to buy car seats second hand as you don't know the history of it.