The chip in UK biometric passports only contains the info printed on the passport, including the picture (some other countries, in particular most EU countries, also have fingerprints but not the UK). I am not aware of any international norm or recommendation to include anything else. So if your passport contains no reference to your previous name (some comments and the passport application instructions suggest that, contrary to your assumption, UK passports would in fact generally include previous names), there is no reason for it to show up when reading the contents of the chip.
The main use for machine readable or biometric passports is to perform database lookups very easily, without having to type anything. In particular, your passport details can be checked against lists of stolen documents (e.g. from Interpol or the Schengen Information System) and your name can be matched against databases of outstanding warrants or lists of people banned from entering or can potentially be used to see your travel history in and out of a specific country (if the country in question maintains a database of entries and exits, which some do).
I don't precisely know what's possible in which country but I guess it should also be possible to search such databases using, say, the date and place of birth and, with a bit of time, to zero in on previous records under another name. So it could be possible to identify you if you somehow attract attention and are selected for secondary inspection, even if the passport does not mention your previous name. But this would not immediately show up upon scanning the passport.
Theoretically, the picture on the chip could also conceivably be fed to some facial recognition software and matched to previous records. But this is more difficult than movies make it look and I would be very surprised if any country was currently doing that routinely.
Importantly, governments obviously don't make detailed individual data about their citizens broadly available to all other countries in the world (think about the logistics and politics of something like that!). So it's just not possible for a random border guard in a random country to instantly get private info about you from the UK government beyond what's already on the passport and its chip. Of course, what's shared with the intelligence services of a few close allies like the US is anybody's guess but that's another matter entirely.