This afternoon I've been exploring Banner Batteries. They don't make it easy to find them, and most battery retailers don't include Morgan in the options drop down.

It seems that 'recent' cars have the Banner 50 200 Uni Bull, which is 58Ah and CCA (Cold Cranking Amps) of 450A. Dimensions are 241x175x175mm and I checked this with a tape earlier.

I found a limited number for sale on line, some at buttock clenching prices.
Here's a decent price though - £80 but the length of guarantee isn't mentioned.
https://www.tayna.co.uk/065-075-078-092-097-Banner-Uni-Bull-Battery-50200-P9656.html

A comparable VARTA is the D21 (075) Silver Dynamic at 61Ah and CCA of 600A with a five year guarantee at £44.97.
Dimensions are 242x175x175 and I don't think the extra 1mm length will be a problem.
Here:
https://www.tayna.co.uk/D21-075-Varta-Silver-Dynamic-Car-Battery-561400060-P7743.html

There's a Black Dynamic here with a bit less performance - 53Ah and CCA 470A and only a 3 year guarantee but at £43.72 the difference in price is so small that the silver spec is a much better bet.
https://www.tayna.co.uk/Type-065-Varta-Black-Dynamic-Car-Battery-P3135.html

DaveW
'05 Red Roadster S1
'16 Yellow (Not the only) Narrow AR GDI Plus 4