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On a Sunday, the first train from Lancaster to Manchester departs at 11:24 (this is the Furness line). On Saturdays this is at 6:24. To Birmingham, the first train on Saturdays is 6:58, on Sundays 11:58. To Glasgow, Saturdays 6:64, Sundays 11:54. The pattern is true elsewhere as well: from Blackpool, first Saturday train departs 5:18, first Sunday train 11:21. Boston, Saturdays 6:13, Sundays 12:13. Lincoln, Saturdays 5:26, Sundays 11:05. It's not true everywhere, but it is in many places. For the rest of the day, the Sunday frequency is not much less than the Saturday frequency.

I've taken the first Sunday train from Lancaster to Manchester twice. Both times, the train was extremely busy. On neither occasion could I find a place to sit. On one occasion, people were left behind on the platform as they could not board the overfull train. Although a sample size of two is small, I will assume this train is always busy.

Considering that demand clearly outstrips supply on Sunday morning, why do trains start running so late?

Since the question was "why", historically in the UK, driver's salaries were quite low, and British Rail ran the Sunday service on an overtime-only basis[1]. That is, only drivers who volunteered (for significant overtime pay) would drive trains on a Sunday. I believe this was similar for other grades of staff.

For this reason, British Rail would only timetable services where they could expect enough volunteers to make it viable to run it on a regular basis.

Nowadays, as many people know, drivers' salaries have gone up massively with privatisation, and in return some Train Operators in the UK have started making Sundays part of the official working week, and no longer voluntary. But the old timetables from the British Rail era often remain relatively unaltered, as many of these Sunday services are loss-making, and the government has not mandated an increase in most cases.

Another reason is that major engineering work is often done on a Sunday, so the timetable is quite often geared towards having long stretches of the railway reduced in capacity (eg down to one track from two, or two tracks from four or six), and so reducing the impact of such work on the number of trains that can be run.

In some new franchises a much better Sunday service is being mandated, eg the new South Western franchise. It remains to be seen whether this will be a common element among new franchises or just reserved for the ones seen as important by the government...

[1] http://www.traindriver.org/what-the-job-involves.html

Trains in the UK are run by private rail franchises who make commercial judgments on when to schedule trains to run on particular lines.

This means that for a line like the Furness line that may have low passenger traffic numbers earlier in the morning on a Sunday the company has decided it is not economically viable to run trains earlier than 11.24.

Other busier lines such as ones into and out of London have trains that start at 05.45 for example.

The various rail franchise holders also have certain service commitments placed on the by the Government when they are awarded the franchises and these vary from franchise to franchise.