Currently I can be given 2 months notice at any time.
This is actually preferable to on the earlier time with this tenancy, where I could be given 2 months notice and also the landlord makes an active decision whether to renew or decline every 12 months.
In fact they always send a no-reason formal eviction notice 3 months before the end of each 12 months renewal as a matter of policy, just to rub it in.
(I would be surprised if that's legal. It seems against the spirit of eviction law where timescales are supposed to begin when a tenant refuses to leave, not months before they are supposed to leave)
On one occasion they did decline to renew, giving no reason. They changed their mind at the last moment after I had a chat with the landlord's property manager. That was a source of great stress for me, not even knowing why.
Eventually I found out. The agency (not landlord) told me, to my face, that they didn't know the why, couldn't get a reason, but the landlord had decided not to renew. But later the landlord's property manager told me that the agency had lied to my face and the landlord did not initiate the decline.
It was the agency who had made the recommendation. I saw it advertised briefly at ~35% raise, so I suspect that was their motivation. These are not rent-controlled, I already pay a substantially above inflation annual raise, so it's not stuck on an ancient rate. If they had got a tenant in to replace me, not only would they have increased their agency fees as a percentage, they would have charged the landlord additional fees for processing a new tenant as well.
Real estate managers are incentivized to change tenants frequently to generate more fees. Sometimes, this also goes against the interest of the landlord as depending on his contract he might need to pay pretty hefty readvertising fees.
See the section near the bottom starting "From 1 June 2019, the only payments that landlords or letting agents can charge to tenants in relation to new contracts are:"
Anecdotally, it seems these fees have indeed disappeared, although few people I know now live in rental accommodation in the UK.
Sure, the fees have disappeared for tenants, but not for landlords! I know because I've been renting myself till last summer. It's a step in the right direction.
In a place such as Oxford or Cambridge you have tons of overseas landlords. Thus, agents are typically extracting fees from them by claiming the tenant has left and the house needs to be readvertised. But, in reality, the tenant wanted to renew the contract. Since they are not on-site, let alone managing the property themselves, it's easy to trick them.
In other words, agents often have a perverse incentive to force a high tenant turnover. Some agents are not like this because they are more ethical, or because they guarantee a minimum income per calendar month. But, on average, it's a very nasty market as you've noted.
Source: Frequently happened to me when I rented.