I suggest PURE Siesta Rise
http://www.pure.com/digital-radio/products/siesta-rise

Comments as follows:

Amongst the desirable attributes I wish to retain a

Large clear LED digits easily read by the short-sighted,
permanently illuminated (no need to reach out and tap anything),
also displayed when the radio is on, but not so bright that they
light the whole bedroom.

The Rise has very large time display (which I can read without glasses
and while half asleep). Permanent illumination is an option and
brightness can be set on a scale of 1 to 5.

At least two easily selectable alarms.

It has three. You can have one for weekdays and one for weekends.
Unfortunately you cannot differentiate between Saturdays and Sundays.

Radio when used as alarm to be the same volume as when last
listened, which can be set as low as I want.

You can set the radio volume (for when the alarm activates) on a scale
of 1 to 32. You will know level when last listened to so you can set
it the same.

Control buttons easily located and operated without my head
leaving the pillow, ideally on the front.

They are on top as the display occupies the whole front. It would be
better if they were were tactile for feeling in the dark but you get
used to where they are.

Sleep timer with adjustable duration.

15 minute increments to 60, then 90

Mains operated, with automatic clock synchronisation.

Mains or battery operated. Synchronisation can be digital only, FM
only or digital and FM.

Setting not requiring navigation through lengthy menus.

Depends what you mean by 'lengthy'. You obviously have to go through
the various options if you want a radio that provides options.

I guess for future-proofing DAB should be included.

DAB and DAB+.