Hello again , 2000 is considered the bare minimum, at which a tent is considered waterproof.
Some tents have a HH of 1500, which is considered to be 'showerproof', not sure what you do with those excepf pray for good weather.
So the higher the HH the better, however loads of people have tents with a HH of 2000 and they are fine, even in very bad weather.
However the higher the HH of your tent, the less nervous you are going to be when a huge storm blows in.
We were in a horrible thunderstorm last year, and our friends were worried that their tent was going to leak as it was a bit of a cheepy, we all went to the pub for dinner to sit out some of the rain and when we came back their tent had blown away!
2000HH is "okay" but I personally would want at least 3000HH for the UK
Also (speaking generally here, there are always exceptions) 2000HH is typically found on lower quality tents & 3000HH+ on tents by the long standing, well known tent manufacturers, so as WTWTW says, leaking might not be your only problem!