I think you can use them with confidence - I haven't used them myself but they're very well known among vinyl lovers in the US and have a very good reputation. You might also want to check out Elusive Disc and TheMusic.com.
Until very recently, with the pound sterling at $2, it could be cheaper buying LPs from the US than from the UK, even after taking postage into account. That's not so common now. You certainly wouldn't want to buy a European LP (eg Speakers Corner) from the US but it might still make sense to buy a US LP (eg Classic Records or a Warner/Rhino reissue). It all depends on the postage - and also, critically, whether you have to pay import duties. You are liable for import duties on anything costing over £18 (excluding the postage) but worse still, once Customs & Excise are involved, you have to pay your delivery company a handling fee for clearing the item. With some companies this is extortionate - worst of all is ParcelForce, which charges an incredible £13.95, so if your US delivery company is using ParcelForce as its UK partner, keep well clear.
In short it's probably not worth buying from the US unless the goods cost under £18. But if you're after a Classic Records LP, do check out TheMusic.com. Most of these Classic LPs cost less than £18 in dollar terms and TheMusic.com offers a free hand select service whereby they inspect the LP before despatch. They also have very cheap delivery to the UK.