which in your opinion would be the most profitable (so basically having the best business case ratio, cost benefit analysis etc.) lines in the UK to be electrified.
Start with almost all lengths of track that carry 6tph or more. There are not many places with this intensity that are not already electrified, but I can think of Dore-Sheffield; Stourbridge-Dorridge; Chiltern mainline south of Bicester. I assume there are other 6tph lines around Bristol and Leeds that are long enough to recharge a Battery-powered BEMU.
Once this programme is committed, plan a cascadable national fleet of BEMUs that can be configured as short-range BEMU (e.g. 40 miles guaranteed range); long-range BEMU (100 miles guaranteed); tri-mode with biodiesel range extender. Perhaps top speed of 110mph on the wires, around 70-90mph on battery.
Plan the BEMU roll-out to exploit existing battery opportunities (e.g. Windermere; CLC; East-West Rail or Didcot-Oxford) and committed electrification programmes (e.g. Matlock; Liverpool-Nottingham; Kidderminster-Stratford). You can't assess other electrification proposals until you've got a Battery strategy.
At the same time, convert fully-electrified mainlines (e.g. ECML; MML etc.) to pure EMU and cascade their 80x electo-diesel bimodes to routes that are only partially electrified (e.g. Chiltern; XC)
Then electrify the mainlines carrying 4tph or more (e.g Chiltern north of Bicester; Bristol-Bromsgrove; Birmingham Derby: there must be others), and start to build recharging islands at network nodes beyond the range of existing electrification (e.g. Salisbury; Worcester; Exeter-Taunton; Lincoln)
Throughout the programme look for opportunities to extend electrification cheaply to reduce miles run under battery, by lengthening OHLE run-outs to the first overbridge or by feeding recharge zones from existing OHLE schemes (e.g. around Warrington Central; Newark Castle; Retford low-level).
As you roll out electrification, grow the EMU-only fleet in the core network, releasing bimodes and BEMUs to service the periphery and progressively cascade the existing diesel fleet into the wilds of Lincolnshire, Cornwall and Wales.