What's your current rate, when does your product end and is the £208k your current balance?
When do you expect to receive the inheritance?
If you're still on an old cheap fix, you'll get a much higher interest rate by saving the money until the end of the fixed rate period. The extra interest will go a long way towards paying off the extra £8k. You'll also be reducing your balance due to normal payments.
For example, if your current mortgage rate is 2% and you can get 5% on savings and you get the inheritance a year before your fix ends, in that year, you'll earn £10k in interest, which will be taxable, although you can reduce this using your ISA allowance. If it's a joint mortgage and you are married, and you get the inheritance before the end of the tax year, you could put £80k in cash ISAs, which would reduce the tax quite a bit.
But if the overlap is smaller so you don't earn enough interest to pay the mortgage off, when the fix ends, I would pay off most but not all the mortgage, partly because minimum mortgages are somewhere between £25k and £50k, so you want to leave this amount, also so you have some savings (assuming you don't already have a decent amount, or else you'd just top up the £200k with savings to pay it off and wouldn't be asking the question).
Then you want a mortgage with no arrangement fee and no early repayment charge. Interest rate is secondary, you might decide to stay with the same provider for ease, or you might decide to go elsewhere for a better interest rate. But you'll be able to match most of the interest with that you earn on savings, so it's a minor consideration. I'd also assume that you'll be able to overpay the £30k (for example) as obviously the monthly payment on a £30k mortgage will be much lower than a £200k mortgage, unless you reduce the term, which I wouldn't, if you get a mortgage that allows unlimited overpayments, because you can just overpay.
Or, something else you could do to free up money to pay the mortgage off cheaply, which would work if the balance is a few £k is to get the money onto a 0% credit card, eg by taking out a 0% spending card and putting some of your normal spending on it, or transferring balances. You can usually get cards with 0% for a year or two with no fee. This is what we've done. We've never had a fix rate so, while we benefited from a virtually interest free mortgage for over a decade, when rates started to rise, it wasn't worth fixing as we didn't owe very much, so we overpaid most of it and shuffled money round so now have about £12k on a couple of 0% credit cards and are saving to pay them down if we can't get new offers, but are profiting from the interest in the meantime. But only go down this route if you know what you're doing and don't spend for the sake of it.
If you've fixed after rates have gone up, and you can't match/beat the interest with savings after tax has been accounted for, then you'll need to consider whether it's worth paying an early repayment charge to pay it down. That will depend on the interest rate and the size of the fee.
A final consideration would be if you want to do anything else with some of the money - home improvement, car replacement, big holiday, pension top up, that sort of thing. Which would obviously increase the amount that you end up having left on the mortgage.