Bradford is tricky to compare, because if you look at the "urban area" stats it's grouped with Leeds. If you look at the "city proper" stats it's just behind sheffield, but "city proper" stats can be quite misleading about the size of a settlement (London is down near the bottom of Wikipedia's "city proper" list).
For comparision I'm going to take the top 9 cities on Wikipedia's "City proper" list and arbitarily add London to the top, since "City of London" is a ridiculously narrow definition of London* to get a "top 10 cities" list.
* London
* Birmingham
* Leeds
* Glasgow
* Manchester
* Sheffield
* Bradford
* Edinburgh
* Liverpool
* Bristol
* London has direct trains to all cities on that list, though those to bradford are infrequent.
* Birmingham has direct trains to Everywhere on the list except Bradford.
* Leeds has direct trains to London, Birmingham, Edinburgh, Manchester, Sheffield, Bradford, Liverpool and Bristol. It misses direct trains to Glasgow..
* Glasgow has direct trains to London, Birmingham, Manchester, Edinburgh. It has one direct train a day to Leeds, Sheffield and Bristol and three trains per day to Liverpool. It has no direct trains to Bradford.
* Manchester has direct trains to Everywhere on the list.
* Sheffield has direct trains to London, Birmingham Leeds, Manchester, Edinburgh, Liverpool and Bristol. Like leeds it misses direct trains to Glasgow.
* Bradford has direct trains to London, Leeds and Manchester, though those to London are infrequent. It has no direct trains to Birmingham, Glasgow, Sheffield, Edinburgh, Liverpool and Bristol.
* Edinburgh has direct trains to London, Leeds, Glasgow, Manchester, Sheffield and Bristol. It has one train per day to Liverpool, It has no direct trains to Bradford
* Liverpool has direct trains to London, Birmingham, Leeds, Manchester, Sheffield, It has a few direct trains per day to Liverpool. It has no direct trains to Bradford, Edinburgh or Bristol.
* Bristol has direct trains to London, Birmingham, Leeds, Manchester, Sheffield, Edinburgh. It has no direct trains to Glasgow, Bradford or Liverpool.
In summary Bradford is by far the worst connected top-10 city in terms of direct trains to other top-10 cities.
\* Heck most of the London stations aren't even in the "City of London". That gives us a "top 10 cities" list of