Depends - was it a paper application or online?
Was there a Will?
Any unusual circumstances - not all executors taking the grant? Issues with the Will? Anything extra adds on a couple of weeks at least.
Looks like you submitted an IHT400 - HMRC are currently saying leave 4 weeks between sending the IHT400 to them and sending the application to the Probate Registry (usually it is 3 weeks and I think it still says that online) as they email the IHT421 directly to them.
Sometimes HMRC will send you a letter saying they have sent the IHT421 to the probate registry and sometimes they don't.
I have had recent online applications back in 3 weeks and others in 17 weeks+. There seems to be no rhyme or reason for it.
The main issue/ hold up seems to be the delay between the probate registry receiving the documents, scanning them in, matching them to the IHT421 and allocating them to a team- from my online system (I am a solicitor) it looks like that takes around two weeks. If it works smoothly then it is fine but it is horrendous if something goes wrong (like a recent case of mine where they had failed to scan in one page of the Will correctly - it took 2 months to rectify).
I would call them in 3 weeks' time to check they have everything as I find that they will not contact you for ages to say there is something wrong/ missing.
Good luck! When I started out we used to get grants back within a week - 10 days. Those were the days...