“Conserving Historic Vessels” suggested that searching Lloyds Register and Lloyds List for references to a ship were often worthwhile. This proved to be the case.
Lloyds Register of Shipping (accessible for between 1930 and 1945 here: www.plimsollshipdata.org) provided the following info. The explanations from the categories I have included were taken from the Plimsoll site. This has records for Beta III from 1930 to 1943 displaying basic info on length, engines and purpose.
The 1930-31 entry:
The 1943-4 entry:
If anyone has any experience with interpreting these listings, please let me know. It is mostly in code and fairly impenetrable.
Official number – 148716
(A number allocated to a British ship when first registered and which does not change over its British career, even if its name or owner changes.)
International code signal – LCMR
(A unique four-character code which a ship could use to signal its name by a flag hoist or by radio)
Material, rig, machinery – “TwinSc. Par Mot. s8Lon.No.8-11,87” Not sure quite what all that means!!
(By 1937, most ships were steel, so only other hull materials (wood or iron) were noted.)
Tonnages – 44 tonnes gross, 36 under deck, 20 net
(Gross tonnage is a measure of the total enclosed space in a ship. Under deck tonnage excludes any superstructure. Net tonnage is the space available for carrying cargo or passengers – harbour and other dues are based on this figure.)
Built – 1926, by Edwards & Co Ltd of Millwall
Owners – National Fire Service (London County Council is crossed out)
Registered dimensions – Length 67.1 ft | Breadth 12.9 ft | Depth 5.5 ft
Engines – “Paraffin Motors 4S.C.S.A. 12 cy. 8″-9″. 68 NHP. L Gardner & Sons Ltd Manchester”
On some entries for Beta III there is a maltese cross symbol and 100A1. This means that the ship was built under “special survey”. Whereas 100A1 “indicated the character of the vessel, as assessed by the surveyor”. There is also a “DK” on some entries which suggests a direction finding device.
Any former names of the ship are noted alongside the date of change so I can try and find out if she was ever known as anything else.
2) Lloyd’s List – newspaper reporting shipping movements and casualties
Still haven’t figured quite how to access Lloyd’s Lists. I think they have copies at the National Maritime Museum in Greenwich and may also have copies of surveys carried out by Lloyds. May need to put in a phone call before I venture to deepest darkest south east London.
betaiiifireboat 
Another place to try is the MCA ( Maritime and Coastguard Agency ) .To see what records they hold when she was a passenger boat ( survey’s and repairs ) , the survey’s where done every year.They might have drawings ( plans ) of how she was converted to a passenger boat !
TwinSc. Par Mot. = twin screw parafin motor.
s8Lon.No.8-11,87 I think that is ss3Lon. No 8- 11,37 = special survey 3 London .No8 Nov 1937..
The maltese cross symbol = constructed under Lloyd’s Register survey
100= suitable for sea going service
A = constructed or accepted into Lloyd’s Register class and maintained in good and efficient condition
1 = good and efficient anchoring and mooring equipment
Paraffin Motors =fuel type
4S=4 stroke ( layman’s term ”suck/squeeze/bang/blow”)
C.S.A.= not a clue!
12 cy =12 cylinders (12 pistons )
8″-9″.=8” diameter pistons with a stroke (how far they move from the bottom to the top of the cyclinder ) of 9”
68 NHP = 68 horse power (the N = the way it is worked out)
Correction I got s8Lon.No.8-11,87 wrong .It should read” I think that is ssLon. No 3- 11,37 = special survey London .No3 Nov 1937.”
1DK = 1 deck
ELEC Light = Big carbon arc spot light on the bow
Thanks Rob – very useful indeed! I knew someone would be able to decipher! Am going to update the post and have a look at some of the suggestions for more research. A previous survey and some plans would be really useful!