OP was driving along happily - and chose to accelerate to avoid others causing an accident - no panic involved
it was cars joining the dual carriageway.. not taking part in a destruction derby, they managed to join with whatever cars were behind OP so your point there is pretty moot.
you misunderstand the law - the responsibility is on the joining traffic to do the adjusting
I'm not misunderstanding the law, the onus is on joining traffic to adjust their speed accordingly NOT to wait until the road is clear before coming out, it's not a give way, the nature of sliproads is they are going to pop out either before or after someone that is already on that road, normally depending on their position when they are parallel, if they are in front of you on the sliproad and matching your speed (OP says they were going faster than her actually), all OP would potentially have to is adjust her speed accordingly to maintain her stopping distance, depending how far in front they were she may not have even had to do that.
So no, you of course don't give way or zipper merge with people joining, but you shouldn't be braking or accelerating off either, or doing anything erratic, maintaining your speed and trajectory while adjusting for stopping distances being compromised by joining traffic is what you should be doing.
OP didn't carry on as normal, she quickly accelerated to get past them, this time it worked out okay, but if there was an overtaking car pulling in in front of her at the time she decided to so that, or if one of the cars on the sliproad had clocked her before she put her foot down and accelerated to get out in front, it could have caused an accident.. and it was all completely pointless.