Do they have commercials during shows in Britain?

Depends on the channel...

BBC = No commercials, as publicly funded national broadcaster with an extortionate licence fee. (BBC1, BBC2, BBC3, BBC4, BBC News, BBC Parliament, etc)

ITV = The UK's first commercial broadcaster, shows adverts.... roughly around 2-3minutes of adverts every 15minutes on most standard shows (e.g. Soap operas, etc)... with one between the shows, and another half way through.... with a bit more flexibility during sports like the FIFA world cup to accomodate half-time (between shows ad, pundits blethering on for a bit, adverts, bit more blethering on, introduce the commentators, start game, half-time, adverts, blethering from pundits, adverts, return to start of 2nd half of match, full-time, adverts, post-match blethering, adverts, blethering + interviews, outro titles, adverts prior to next show)

Channel 4 = The UK's part commercial / part national broadcaster introduced during the 1980's... works commercials same way as ITV

Channel 5 = Introduced around late 1990's as the UK's 5th free to air terrestrial broadcaster, also works the adverts same way as ITV.

Assorted channels on Satelite (Sky + FreeSat), Cable (Virgin) + the FreeView Digital Terrestrial system (full service transmitters only), such as Yesterday / Discovery / Quest / Smithsonian / Comedy Central / Sky One, etc = also mostly use the system used by ITV.

There was briefly an "ABC1" channel that ran from 2004 to 2007 that had things like re-runs of Home Improvement + other ABC shows from the US before it left the UK due to disagreements about positioning in the epg (among other things)... that ran it's advertising closer to the US method of: 

last  5mins of previous show, start next show to end of opening credits, adverts, re-join show, half-way ads, continue show until last 5minutes, adverts, finish show, start next show... think I saw "SciFi" / "SyFy" channel do something similar back then too.

The BBC, which I believe is the most prominent broadcaster, does not have commercials since it is supported by tax revenue.  Other, privately owned, networks in Britain do have commercials. 

Certainly they have commercials...but the BBC does not.

I quote:

In the UK, the BBC is funded by a licence fee and does not screen adverts. On the commercial channels, the amount of airtime allowed by the UK broadcasting regulator Ofcom for advertising is an overall average of 7 minutes per hour, with limits of 12 minutes for any particular clock hour

To say that in terms we Americans understand

everyone in the UK who has a television

has to pay for the BBC

(really: for the privilege of being able to receive BBC broadcasts, whether or not they watch it).

According to one web site

the current cost is about £154 per year

that is: about US$211 per year.

Non-BBC channels

such as ITV (been around since 1955)

are "free"

but include advertisements to pay the cost of running the network

and so

you can see commercials (and commercial break spots) in TV series produced by ITV.

- Recommend: The Thunderbirds, from the 60s, but many others you are likely to know, such as various Agatha Christie series.

BBC shows don't have commercials- however they may have "ad" for programs coming up or on streaming/dvd

There are Several TV stations in the UK that do  have commercials- usually they will end 5-10 minutes early and PBS puts in short films or trailers for their up coming shows.

Example: Downtown Abbey was Not made by the BBC but ITV and would have had commercials when aired in the UK.