Train Operator Websites

Just the ticket

You can use any of these websites to book tickets for any National Rail journey in the UK. You aren't limited to the operator's site for their own trains, and be aware of third party websites because they often charge booking fees, while the websites run by actual train operators generally don't.

Doesn't ask for title at all

• Chiltern Railways - chilternrailways.co.uk
• Grand Central - grandcentralrail.com

Title is optional

• Avanti West Coast - avantiwestcoast.co.uk
• CrossCountry - crosscountrytrains.co.uk
• East Midlands Railway - eastmidlandsrailway.co.uk
• Greater Anglia - greateranglia.co.uk
• London Northwestern Railway - londonnorthwesternrailway.co.uk
• London North Eastern Railway (LNER) - lner.co.uk - mandatory but includes options "None", "Mx" and "Other", which prompts you to add your own.
• Scotrail - scotrail.co.uk
• TfL (Oyster/Contactless account) - account.tfl.gov.uk - has "Other" as title option, but doesn't require any entry
• TfW Rail - tfwrail.wales
• West Midlands Railway - westmidlandsrailway.co.uk

Title is mandatory but custom titles can be entered and/or "Mx" is an option

• Gatwick Express - gatwickexpress.com
• Great Northern - greatnorthernrail.com
• Great Western Railway (except Night Riviera) - gwr.com
• Hull Trains - hulltrains.co.uk
• Merseyrail (day savers only) - merseyrail.org
• Southeastern - southeasternrailway.co.uk
• Southern - southernrailway.com
• South Western Railway - southwesternrailway.com
• Thameslink - thameslinkrailway.com
• TransPennine Express - tpexpress.co.uk - Bonus points from me for rebranding some trains to "TransPride Express" during Manchester Pride festival.

Title is mandatory and only offer gendered titles

I will be contacting these companies soon, or I have done and their response is included.

• Heathrow Express - heathrowexpress.com
• Northern - northernrailway.co.uk - Old Northern Rail (Serco-Abellio) site had title as optional. Existing accounts have not had a title forced on them.

For sleeper service tickets, see the dedicated page.

Summary

Going through all these websites in quick succession shows that there's actually only about 4 different booking systems which are rebranded accordingly. Each have their own title options off-the-shelf, so perhaps one changing would prompt the others to follow suit. I will be contacting those listed above who only offer gendered titles to ask them what's up.