Can UK Passport Holders Still Get Single Entry Tourist Visas from Laos?

>Can UK passport holders still get Single Entry Tourist Visas from Laos?

Yes, they can, if they meet the qualifications and the immigration officer is willing to sell one to you.

>Are visa exemptions by crossing into Laos and back to Thailand again still allowed?

Yes, you can use most Lao borders to cross over (the ones that are closed you never heard of). You can cross over twice in a calendar year. Each time you cross you get a 30 day visa exempt, extendable by another 30 days at immigration.