Steve1979,
Since you’re in the UK, when funds permit, buy a Knosti Disco Antistat for about £40 if you want better results than your just acquired cleaning kit can offer. It’s not offered here in the USA, so I’ve never used one, but from everything I’ve read you should get excellent results if you use it with distilled water.
Please do not use tap water. Distilled or deionized water is much better for your records since it won’t leave any minerals behind when it dries.
Proper wet cleaning is always going to work best, but I would not risk completely submerging your records and ruining (some of) the labels by needlessly getting them wet!
Here in the USA we have the SpinClean, which is a useful manual wet cleaner that sells for about $80.
I started out cleaning with a Spin Clean, and now use Audio Desk and Klaudio ultrasonic record cleaning machines ($3-4k each) and offer a record cleaning service to others as Record Genie.
I’ve got happy customers who send me records from all over the USA since we have cheap Media Mail postage, but you might look for someone who offers a similar kind of affordable service in the UK.
Good luck in your quest for clean records!
Dave