Yeah, that's my guess for the price too for the new iPhone SE.
Unfortunately, the OP has a max budget of £300.
I wasn't making the SE/9 an option to buy but it's fairly obvious that the release of that phone will affect the third party retailer price points who currently stock the phones that Apple discard. Apple will probably quietly allow them to sell for a price that will degrade over the coming year in normal circumstances - we don't really know what will happen to demand this year though.
You can assume that iPhones 7 and 8 will continue to get manufactured to quietly fill the gaps that Apple won't officially fill on their website though and I expect the 6s models to quietly disappear as a brand new product.
I bought my 4" SE brand new for £219 a couple of years ago, and prices continued to fall after that, with even a 128Gb variant becoming available for something like £249 before it finally disappeared as a brand new to buy product at certain third party retailers. This will have been a little under 2 years ago now.
For the sake of example I would not be surprised to see an iPhone 8 for as little as £279-299 within 12 months time. It could well re-appear for as little as £349 at third party retailers from next week in my opinion.
Truthfully, even after the new iPhone SE comes out, I suspect it's going to be difficult to find an iPhone 7 Plus 128 GB or iPhone 8 Plus 64 GB for that £300 price, unless it's refurbished. iPhone 7 Plus 32 GB may be within reach if he stretches that budget a bit, but 32 GB can be rather limiting for many people.
Either way though, it does make a lot of sense to wait for the new iPhone SE release before making any decisions, to take advantage of the expected price drops on older models. I'm expecting the new iPhone SE to be announced this coming week or else next week.
I keep an eye on third party retailers in the UK - my 4" SE 32Gb is the most advanced iPhone I have ever bought, and I got it nearly a year after they doubled the base storage from 16G to 32Gb as the price slid at third party retailers - rather than buying it list price from Apple. The OP hasn't mentioned how much storage he's after but obviously at the lower budgets the increased storage SKUs make less sense as they take up a higher percentage of unit cost.
For under £300 post iPhone SE/9 I'd be looking for a 32Gb iPhone 7 Plus (which like the 8 Plus comes with 3Gb of RAM) at some point later this year. It's currently £389 at Giffgaff.
Remember these are street prices so individual retailers will vary:
Assuming the SE/9 is £429 with 64Gb I'd estimate the base 8 (64Gb) to be £349 with the 7 (32Gb) dropping to £249.
The 7 and 8 plus models would be £100 uplift on those, and anyone wanting 128Gb would pay an additional £50-70.
From that point on UK retail typically makes shallow prices cuts every few months (eg £10-20) for the next year until the next phone comes out.