Hi K4N3Y,
the 'B L CARS' plate was fitted to 1980-1983 years approximately so your car is an early 80s model and is a Mayfair or HL etc, not a basic City.
From late 1980/ early 1981, the vin started SAX_XL2... so your car probably pre-dates this and would have likely been on an 'X' or 'V' registration.
Like Nick says, the 031001 number is a type approval code and means nothing to an individual car. Everything you need is in the long XL2S number- it doesn't matter that there's no spaces as the numbers are mostly a serial number.
You can apply to the DVLA to get a logbook with form V62, available here - https://www.gov.uk/g...certificate.pdf
Leave the section with the number plate blank and maybe include a note explaining that the plates were missing/ stolen etc when you bought the car. This service costs £25 and involves the DVLA writing to the previous owner, therefore it takes a few weeks but there's nothing to be concerned about if you are the legitimate owner of the car.
However, if you want to message me the VIN I can tell you if it's still on the DVLA computer and also tell you the registration number.
I went through this whole process with my 1971 Range Rover. It had been 'plate raped' (for want of a better phrase...) in the distant past; someone had removed the VIN/ I.D plate and number plates from the car and fitted them on to a (presumably later) vehicle, probably to get free road tax. I didn't know the registration number but fortunately, Range Rovers have the stamped VIN stamped on the offside chassis leg, so that was my way of claiming back the original registration.
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