Hi @SmartHome, I use the benchmark of the full loan (living away from home outside London and available to those students with domiciled parental household on low income) of £9,706 and see where the most abundantly available first year uni accommodation and typical private rents in second and third years gets you.
On this basis, you can live within that budget, across your uni degree, in the cheaper Midland and North of England cities and towns. It is much harder to do so in the South generally; that makes intuitive sense but means those on tight budgets (students and parents) need to be aware. Students don't necessarily have to change choices but will have to have a plan to deal with the inevitable financial shortfall, so being aware and talking about, as we are here, is very sensible.
People will say that, even in 'expensive' locations, there are cheaper options and whilst that is the case, the cheaper option often is not really what might have been reasonably expected when digesting the various unis' marketing output. Did you select St Andrews to live in Dundee? Probably not. Did you realise that U of York has very little budget first year accommodation so you may have to take an expensive ensuite on the East campus? Probably not.
In relation to your specific questions re: Southampton and Lancaster, I'd suggest you take a look at the accommodation pages on the respective uni websites. These will give some sensible benchmark costs and links to SUSU lettings and Lancaster University Homes. The good news is that both unis have abundant first year accommodation, to the extent they can guarantee accommodation for those putting their uni as 'insurance'; Lancaster also guarantees campus accommodation for 4th years returning from placements and has also worked hard, alongside Uni of Cumbria, to ensure a sensible supply of uni-owned, private and institution stock on a 'whole-of-town' basis; this puts Durham - another small town with a large student population - to shame, to be honest.