https://www.highwaycodeuk.co.uk/joining-the-motorway.html

Joining the motorway.

When you join the motorway you will normally approach it from a road on the left (a slip road) or from an adjoining motorway. You should

• give priority to traffic already on the motorway
• check the traffic on the motorway and match your speed to fit safely into the traffic flow in the left-hand lane
• not cross solid white lines that separate lanes or use the hard shoulder
• stay on the slip road if it continues as an extra lane on the motorway remain in the left-hand lane long enough to adjust to the speed of traffic before considering overtaking.

You're meant to give way on a slip road. So if you can't merge safely then you have to stop. You're the bad driver here not them.