Ah Gordi,
I can appreciate the anguish here as I spent years trying to track down my parents original Beta Saloon which had alledgly been sold to a "Lancia Enthusiast" in June 1989 so I felt it was in with a sporting chance of survival - but it soldiered on for another 3 years before going untaxed from 1992 onwards. Your story has touched me as it really does mirror my own Beta story. The Beta left such an impression on me at such a young age it is quite simply the reason I became a car enthusiast and why I waited so long before buying my Betas and jumped at the chance to buy another Beta Saloon from the exact model year specification!
To help, I can offer the following points:
* Looks to be a Series II FL Coupe made from 1979 onwards judging by the frontal appearance and your mention of the later dashboard.
* The colour is almost certainly going to be Verde Ascot (Ascot Dark Green) 109 which would have been paired with the grey woolcloth interior - I know of two surviving Beta Coupes in this colour specification and both are registered later than this which rules them out - but this doesn't mean to say that further examples aren't surviving out there.
* Judging by the last letter of the first part of the reg is almost certainly a "K" so you have that to go with and the "V" Suffix.
London Lancia Dealers in 1979 / 1980 were:
NW2 Broadway Autos 50-56 Cricklewood Broadway Cricklewood
NW7 Maurice Fraser, Hartley Avenue Mill Hill
W1 Portman Garages, George Street, Baker Street.
W4 The Chequered Flag High Road Chiswick & Colville Road Acton W3
SE1 Waterloo Carriage Company - The Cut - Waterloo
SW1 Peter Wolfenden - Horseferry Road - Westminster
SW10 Len Street - 67-69 Drayton Gardens Chelsea
SW19 Ivor Hill Dursford Road Wimbledon Park
Service Agents were:
Chipstead of Kensington - 6 Stamford Brook Road W6
DB Autos - Tinworth Street SE11
Belvedere Carriage Company - 11-15 Plumstead High Street SE18
Talon Engineering - 21/3 Basing Street W11
BWB Motor Services Heddingham House 53 Clapham South Side - SW4
Robert Patrick & Partners 10 Manson Mews Queens Gate.
I'd also add Broadfields at Cockfosters (more famous for selling Land Rovers and Jaguars) and Formula Autos Tottenham and HR Owen to this as they all had Lancia franchises around that time - maybe a little later.
Might be worth including the Hertfordshire dealers here too due to the proximity of South Mimms
C - Way Autos Beaconsfield Road Hatfield
As you say, probably a long shot that she is still out there 40 years later, but you never know - I find it is always surprising what comes out of the woodwork.
If thise leads you to finding it or not finding it as the case may be I can thoroughly recommend rekindling your love of the Beta with owning one

Alex