To not want to pay off my mortgage?

Hhhmm. If the MIL wanted to make a £50,000 gift, specifically to pay off some mortgage debt, then this is a kind and generous offer that on the face of it, most people would snap your hand off for. But the issue here is that the gift is being offered with the proviso that you match her contribution.

My worry here is that the gift isn't really a gift, its a hook to maintain control of your finances and limit your ability to make your own financial decisions, which as an adult with capacity, is your absolute right.

If it were me, I would spell out to her, that you are extremely grateful and such a gift would have a huge beneficial impact, but you would be in a more robust and nimble financial position by retaining £50,000 as an emergency fund while using her generous gift to reduce the mortgage debt to the point where interest is minimal, allowing the principle to be repaid a lot faster. Her responses, I think, will offer a window into her true motivations.

It comes down to what degree you are willing to hurt yourself financially to maintain your independence and agency. Everyone has a different red line on this, but there is a point where you say "thanks, but no thanks" and go your own way safe and secure in the knowledge that every penny you have is off your own sweat.

I think they would if it came with a free £50k

THIS is an extremely valid reason for not paying off the mortgage.

(The rest of the reasons are rubbish and make no sense).

Well no, because they'd be trying to sell you investments. So not really a great measure of whether it's the "right" thing to do.

I would probably invest some in my mortgage, hopefully they would still match it, say 30k to the mortgage and 20k savings.

I’m with you, OP. A relatively small mortgage and a decent amount of liquid cash would always be preferable to me. I don’t personally get the obsession with paying off a mortgage, but each to their own.

Rubbish.

A gift with strings attached is not a gift at all, it's a way to exert control over someone.

We have a similar situation. An inheritance that would pay off our mortgage but like you, our mortgage is manageable so we have decided against paying it off. We would never be able to save this kind of money up again.
We might pay 1/3 of the mortgage off when it's due for renewal in 12 months and aim to reduce the term but we like having some savings available.

I get that it's about the strings. Sometimes they aren't worth the money for the way they affect your life and independence, ime.
Plus it might not be financially sensible at the moment - is your interest rate lower than your savings rate?

Don't be blackmailed. Do whatever you want with the initial £50k and tell your MIL thanks but no thanks.

This is the reason that makes sense to me.

Worrying about frittered away income that would have gone to mortgage could equally apply to frittering away the lump sum and you miss out on the further £50k.

But if the level of interference is unbearable then that's a NO. But it seems DH allows this anyway so if he does why not be £50k better off and save mortgage interest.

Perhaps set up a standing order to a savings plan that only allows a couple of withdrawals a year? Or even explore offset mortgages where the savings offset the mortgage savings you interest. With the total amount offset you pay no interest and the monthly payments pay off capital

If it is this then it would be a No from me. As great as being mortgage free is (we are) you might need some cash for an emergency and it will take a while to build up a nice amount of savings.

You’ve never had someone controlling your life with money.
Op has obviously got previous experience of these generous acts.

I would - and ignore any rubbish "strings"

I would also set up a direct payment to a savings account of the amount you would be paying

You are potentially turning down 80K (50k from MIL, 30k saved interest).

Only you know if the back story is worth that.

Is it £100k outstanding and she will only give her £50k if you use your £50k too? So effectively having to use your savings as directed by her?

Op doesn’t want the gift.
If I’ve read this right.
Op has her own £50k that she wants to use for other things.
The mil wants to match the £50k and insist the £100k comes off the mortgage.
Mil has no say over the nest egg, that’s for op and her dh to decide.

We paid our mortgage off a couple of years back … gives a lovely sense of freedom and security. For example, lots of shenanigans at work at the moment, possible restructures and redundancies .. and I am as calm as you like, as I don’t need to worry about paying the mortgage.

How you can say it’s not really helping has me baffled

It is a help and it’s very generous- they are offering to clear your mortgage fgs

it is your thinking that is off not theirs!!

If you pay off your mortgage, you can still move, you'll just have more equity in your house to put towards the new house.
I paid off my mortgage in my mid 30's (small mortgage) but then set up a standing order for the mortgage amount to be paid into a savings account. I didn't notice the difference on a month to month basis but it built up into a large sum which gave me security.
This gives freedom for the future.

We could pay ours off, but have the money invested at a much higher return than the interest rate on our mortgage so it would be madness to pay it off

It doesn’t matter what you want. Your mil wants to give you the money to pay off the mortgage so that’s where it goes. When you accept gifts from others you need to accept their terms too.

I'd pay it off and direct the money elsewhere. It partly depends if you have other debts, savings etc though.