What state are you in? What they are doing may be illegal. In California the rent is on time as long as you pay in advance of the deadline. If you send in six months rent all at once, then you are on time for the next six months.
Also your bank may be able to do this for you. If you add your landlord as a bill pay recipient and set the due date as the 1st, the bank will mail the check on the appropriate day, and if it arrives late, will often cover the late fee.
I just tried this, I opened my bank's app and it took me the whole of 2 minutes to set up a standing order to pay my friend £10 on the first of the month. It would be in his account on the 1st, or the next working day. I pay my cleaner via bank transfer when she leaves my place, and it's in her account by the time she's in the bus. My bank mailing cheques to my landlord is a concept that's just bizarre to me.
Given that you are sending pounds instead of dollars, I'm guessing you live in a civilized place with modern banking and not a backwoods like the USA.
The problem is not technology, it's the USA banking system. We have no way to instantly send money to someone over a few thousand dollars without huge fees. Oftentimes rent exceeds that limit in urban areas.
You can send money via Zelle instantly, but I would stick to check or ACH purposes for legal dispute reasons in the case of conducting business, especially paying rent.
Oh, they've not declared it as a lease violation, they've just asked me to do it this way and I've compiled, despite being annoyed by it. I haven't checked local laws (MA), but I've tried to be a good tenant.
Also, no, my bank will not do this for me. My landlord actually is overseas (permanently), so mailing a check is not feasible.