In the 45 minutes they managed to cover an impressively large amount of ground. Starting with a brief intro on what a cell is (building block of biological organisms, but just like the atom once you look more closely there's a lot more going on inside than you thought), then moving on to how big (not very) and how many in a person (a lot, but even all those human cells still only add up to 10% of the cells in your body, the rest are bacterial). They then covered in chronological order the three main stages in life on earth (if you're thinking from a cellular perspective). First there were prokaryotes - bacteria are this sort of cell. These are the simplest sort of cell - a membrane bag that makes the important chemicals be more concentrated inside than they are in the sea. They have DNA (the metaphor they used was of a library), RNA (copies of blueprints from the library) and proteins (built from the blueprints), and they make the needed energy to do their internal chemistry by transporting protons across the outside membrane. But they don't have any divisions on the inside of the cell, everything's in the bag together.
Then about a billion years later the eukaryotes appear (an amoeba is a single-celled eukaryote) ... and Melvyn Bragg managed to mispronounce eukaryote more ways than I could count in 45 minutes - the best was when he turned it into something resembling "erotic" ;) Eukaryotic cells have subdivisions inside them - they're named for having a nucleus which is a compartment that holds the DNA, they also have mitochondria which were originally free living prokaryotic bacteria. These are the true determinant of eukaryotic cells - they evolved by one cell type engulfing another type, and then living in a symbiotic relationship where the internal bacteria provide energy for the outer cell. It's thought this arose once and only once. So having more energy and having separate compartments (many of them, not just the two I mentioned) lets them maintain a bigger genome (the fragile DNA is kept away from the rest of the machinery, they have enough energy to do more reactions) and do more complex chemistry.
Next stage (after about another billion years) is the arise of multicellular organisms (like people! tho that took a while) - which are lots of eukaryotic cells stuck together. In this last section they managed to touch on the two sorts of cell division, cell specialisation by controlling which genes are switched on or off, and even some relatively recent research that shows that the control switches for the genes might be quite a long way away on the DNA strand so the way the DNA folds up in the nucleus is important (now that's a hard problem to solve)**. Oh, and also to mention the true distinction between male & female (female gametes provide the mitochondria).
The experts on the programme were Steve Jones from UCL, Nick Lane (also UCL) and Cathie Martin (JIC and UEA). Unfortunately Prof. Martin wasn't quite up to the normal standard - she was both nervous & used too much jargon. Either one alone would've been OK, but the two together made her contributions somewhat confusing to follow. Which is a shame, because she came across as someone who knew her stuff (as did the other two) but wasn't comfortable with explaining it to non-scientists (in contrast to the other two).
But that quibble aside, it was interesting to listen to, and I thought it provided a very good high-level run through a complicated subject. It's always nice when things like this hold up even if you already know what they're talking about, gives you confidence that the ones you don't know are equally accurate :)
*Amusingly one of the further reading suggestions on the Radio 4 website for the programme is for a textbook I had to buy for my first year undergrad - Alberts et. al. "Molecular Biology of the Cell" ... it's the 2nd edition I have on the bookshelf upstairs, seems they're up to a 5th edition now.
**One of the things I was doing during my last post-doc was looking for the β-catenin promoter, so this was particularly interesting. Mapping the 3D structure of the DNA to make sure all the various bits line up with the right genes has got to be complicated. And I bet it changes based on what cell type, which other genes are switched on or off etc.