Monzo don’t offer interest on any deposits, and I don’t think they ever will. Even if they do, I’d guess that they’d be pretty low (look at Starling’s 0.5% for example).
The following is my personal opinion. Not investment or other advice!
If you save for a house deposit you’ll likely save for years. With inflation currently around 3% per year your cash will actually loose in value if you earn less than 3% interest. As much as you may find High Street banks antiquated, distasteful, legacy, or whatever, depositing savings there is a much better option, as they will give you up to 5% interest, rather than you loosing around 3% in value each year!
Don’t bother about ISA accounts, though: these currently give terrible returns. LISA, Help To Buy ISA, standard savings account, or standard current accounts are much better options, and you can get up to 5% interest on those (as far as I’m aware), and you can open multiple of them (they often only pay interest up to fairly small balances).
Combine that with current accounts that give cashback on direct debits and/or credit cards that give cashback on purchases (although if those encourage you to spend more, then that’s counterproductive 
), and you can get a pretty decent amount of cash each month - that feels good, and motivates you to save further, and it helps you get your dream home sooner!
Finally, depending on your attitude to risk, consider combining this with investment in the stock market or other assets. Returns can be higher, but you obviously take more of a risk.
Here a few links for further reading:
A recent discussion:
Reasonable savings accounts:
https://www.moneysavingexpert.com/savings/
Reasonable current accounts with cashback, cash for switching to them and/or interest: