Firstly, I don't think anybody can say what the market will be like in 5 years' time. Just about 2 or 3 years ago, nobody was actually aware that there would be an oversupply of law graduates, even though all the signs were in the air. Nobody was keeping track or paying a close attention to the numbers, until now, least of all our regulator.

Secondly, your own prospects are going to differ greatly based on many factors such as your grades and expected class of honours, whether opportunities open up for you along the way through connections or internships, and whether you are an interesting candidate or charismatic or good looking (no kidding).

Personally, I don't think being in a mid-tier UK school will make it more difficult for you, assuming it is one of the still-recognised Scheduled Universities. Firms and the older lawyers like to pay lip service about how the local university law graduates are better, but I haven't actually seen a demonstrable, tangible advantage comes with being a graduate of NUS or SMU thus far. It is pretty even footing.

Lastly, as nobody can say how the market is like in 5 years time, don't get pigeon-holed into the whole cookie cutter path of progression which may not hold true by the time you graduate. You may even find that non-lawyer careers, such as the civil service (outside the Legal Service), are perfectly viable career options and not indicative of personal failure vis-a-vis your peers.