Or switch off "TA" altogether. Again, should be standard in any RDS radio.
The way it works is that when you have selected the TA function the radio searches for a broadcast which has the "TP" (Traffic Programme) flag set. Very often this will happen as soon as you start the car, so it will find a station reasonably local to your starting point, but that depends on the way radio works. In Cardiff, for example, you could easily pick up a station in North Somerset, which is a bit pointless.
The really tricky bit is what happens next, and this depends on how the radio stations are set up.
In the bad old days, independent stations often put "TP" up, whether or not they had any traffic bulletin planned. On top of that they don't implement the "AF" (Alternative Frequency) list properly. Most ILR stations only have one or two transmitters, so often (maybe things are changing in these days of massively syndicated stations, but this is how it used to be) the AF will only list one alternative frequency - the station's other transmitter (if it has one).
Thus as you drive away from your start point the radio will keep listening to that first radio station as long as it is able to decode RDS with any degree of accuracy and only when the signal fails altogether will it search for another station with TP set.
BBC Local radio used to work differently. The AF list will include adjacent transmitters of other Local stations, but some radios won't retune because the PN (Programme Name) is different.
So you are listening to Radio 4, which doesn't usually broadcast TP, and the radio is "keeping an ear on" some other, often quite random station, which does have TP set. Good radios will actually have a second tuner for this job, but not-so-good radios used to dip out every now and then, for a fraction of a second, retuning briefly to the other station. This second radio (or lack of) is also the way the radio determines when it is time to swap to another frequency in the AF list.
When the traffic bulletin is about to be broadcast, and often triggered by the jingle, the transmitter of the TP station will also set TA (Traffic Announcement). At this point, whatever else you are doing is interrupted while the main radio retunes.
ILR would then keep TA active until the end of the sponsor's jingle at least, and often until a little while later, maybe until the presenter had made a link or an ad break had played. Once TA is cleared, the radio will retune to the original programme.
It all sounded very useful when RDS was invented, but it does tend to get abused... which is why any decent radio will be able to turn such functions off.
Hwyl!
M.