Green’s Dictionary of Slang

Melvyn (Bragg) n.

[rhy. sl.; ult. UK broadcaster and author Melvyn Bragg (b.1939)]

1. sexual intercourse [= shag n.1 ].

[UK]R. Puxley Cockney Rabbit.
[UK]B. Kirkpatrick Wicked Cockney Rhy. Sl.
[UK]B. Dark Dirty Cockney Rhy. Sl. 79: ‘Did you get a Melvyn?’ ‘No, she blew me out again.’.

2. a promiscuous woman [= slag n.1 (6)].

[UK]R. Puxley Fresh Rabbit.

3. a cigarette [= fag n.3 (2)].

[UK]R. Puxley Fresh Rabbit.
personal correspondence: Melvyn Bragg – Modern Rhyming Slang for ‘fag’ (cigarette). e.g. ‘Oi mate, can I scrounge a Melvyn off you?’.