I had my babies in 1995, 1999, and 2000. That first one was born in London, the other two in Sheffield. I noticed that all midwives at all the hospitals I went to said, "bath Baby now," rather than "bath your baby now": as others have said, I think "baby" here is used as a name. But I did notice that when we moved to Sheffield, people often don't use the word "the" when I would; but instead they'll introduce other words where I wouldn't use them. For example, my husband's parents (Derbyshire) refer to their daughter as "our Mel", rather than just using her name, and they do this for various other relationships. They refer to my sister as "your Sarah". I find it funny: it implies an ownership I don't feel, but it's very common here.
This is true for University in the UK and Canada as well (people talk about their time at/in University). It makes these things feel more like states of being than specific locations.
In the US we go to the hospital or attend/are at the university (as if there were only one available to choose from), though we do talk about being "in/at college" as a sort of generic, article-less state of existence. I haven't heard that expression used by people from the UK or Canada. Colleges in these countries seem to exist only as entities within universities, never as independent, stand-alone schools. In the US, colleges can be parts of universities (though there are generally fewer colleges per university than at British universities, and they're organized by discipline), but we also have stand-alone technical, liberal arts, or community colleges.
I am English, and have lived most of my life in London. For the last twenty years I've lived in Sheffield, which is in Yorkshire.
We talk about "going to university" rather than "going to the university" because there are several to choose from, and if you're going to use "the" in this context you'd say, "going to the university at Edinburgh"--but you wouldn't say that. You'd say "going to Edinburgh University".
We do talk about going to college: but here, university and college offer very different things. Universities offer degrees; colleges offer more vocational courses, and are more common for people aged 16-18 rather than the 18-22 age band that most universities cater to. Unless, of course, you're talking about the various colleges which make up the universities of Oxford and Cambridge, or Imperial College, which is a London university (my son studies maths there, and it's wonderful).
Bear in mind that there isn't really any such thing as "British speech". I lived in England for three years, and traveled widely, including a lot of time in Scotland. You can identify the birthplace of almost any Brit to great precision by the way they speak, even if they've been to University somewhere. The speech of somebody from Yorkshire, both in accent and regionalisms, is as alien from a Kentisher as somebody from Jamaica is from a person from da Bronx.
caw
This is so true.
Whenever I see the phrase "British accent" I cringe just a little bit, because anyone attempting this is almost certainly going to end up sounding like a parody. You can have an English, Welsh, Scottish or Irish accent: but you're far more likely to have a London accent, an esturine one, a Yorkshire or Lancashire or West Country accent. I have a London accent, but am not broad. My husband has a Derbyshire accent; and our two sons have enough of my London accent to sound foreign in Sheffield, where they grew up, and enough of a Yorkshire accent to sound foreign in London, where our eldest now lives.
The division between the various areas is small. In Chesterfield, people from Sheffield are sometimes called "dee-dahs" because of their accent, which is very different to the Chesterfield accent: but I can drive to Chesterfield from here in less than half an hour. It's not far away.