Sadly no government price fiddling - it might not be so painfully expensive to live here, if there were! I’ve just found a flat in London and it’s been a pain in the arse looking, so I feel for your friend…
I think turnover of tenants is quite high in London - people tend to move around a lot, whether for work or studies, or just because they feel like it, I think (though that might just be people I know…) - and Dervorin is right, she needs to be able to pay a holding deposit on somewhere then and there if she likes it (and is going through an agency), or commit instantly if she’s doing it through a private landlord. Otherwise someone else will, and she’ll lose out.
I found Streets Ahead were really proactive in calling me with details of flats and arranging viewings for me, though their agency fees are a bit steep (at least, compared to other English agencies; I was moving from France where the standard is a full month’s rent, so cheap in comparison to that!) - I ended up taking a flat with a private landlord that I found on Gumtree, though, just because I could move in instantly.
In fact, I think I’ve found all my flats in the UK on Gumtree, though there are now a much higher number of scam postings than I remember there being a couple of years ago, so if she goes that route, she should remember to run a mile from anyone who even mentions the words Western Union, no matter how nice they otherwise seem. (I should have known, really, from the low price and lovely flats - but they weren’t that low a price that they automatically pinged my radar as scams. At least, not the first couple of times - after that, they were more obvious. I’m clearly a bit slow
)
Liverpool St is the wrong side of London for me, so I know nothing about what areas might work for her - but if she looks along the major commuter lines, starting in about Zone 3 or 4 and moving outwards she should find something that’s a fairly reasonable balance between price and travel time. (Unless she’s paid a fortune, in which case, she needn’t wait til Zone 3.)