I "routinely" do this to feed my addiction, but as we all know addicts do stupid things

I have used HGSS recently; their service is prompt and efficient although getting communications started can be a little hesitant.
HGSS requires a little less paperwork than other UK RFD exporters if have used - I don't know the reason. Maybe there is some sort of pre-clearance on their part? Anyway... not my problem. Others can be a little cheaper but you wait longer for papework to clear in the UK (including assurances you will not be using components to assembly nuclear weaponry ... damn - there goes my master plan : ) ).
Moving on.. Your challenge, if you decide to accept it, is twofold: BATFE and ICE/CuBE ("customs").
You will need to either.
1. Obtain a Form 6 Permit from BATFE for import under your Type03 (Curios and Relics) licence
2. Proove to "Customs" that they are antique and self import
3. Use an importer.
Note that getting the Form 6 requires proving age - usually possible for most UK guns using a reference like Brown's if the gun maker is not documented anywhere then that's a roll of the dice. Regardless you'll need to follow up with a 6a proving importation, and legally you'll have 2 weeks to mark the gun(s)with origin information as detailed in the 6a.
This process can be done as quickly as 2 months or as long as 6 or so. The Form 6 is valid for 2 years after issuance.
If you import yourself under a Type03/Form6 you will have another hurdle to clear with "Customs" - bonding. Law requires posting of a bond. You will need to work with a broker on this.
The added inconvenience is that over the last few years everything has become electronic (well, almost everything). The impact of this is that the clearance for bonding etc. is sent electronically; that more or less requires a broker/bonding agent since they are set up electronically in the system.
One final note that sound facetious but isn't. Everytime I do this I have a different experience at ICE/CuBE depending which officer is at the desk that day. There is a LOT of officer discretion on what they ask for or tell you to do. I've spent two days clearing a shipment going through the full hop skip and jump routine and I've spent 10 minutes.
The advantage of an importer/broker even if you're set up to do this yourself is that they handle all the pain. Of course they charge you for the pleasure but there you are. The unspoken reality is also that the ones who do only this for a living know whichi officers to interact with and which it avoid if possible.
As to costs, well HGSS or whoever can tell you. As a crude rule of thumb for low volume cheaper guns I guess at double the auction cost to get it to your door. Fees generally total a few hundred at ICE/CuBE and a few hundred in the UK.
Are you feeling lucky? Well, are you?

Jeremy