My brother owns a house and has two lodgers renting rooms. He’s asked them to leave and they refuse.

If the renters have to share the kitchen or bathroom with the owner, their child, spouse or parent and if the room that they are now occupying is locate at your brother’s principle residence and he lived there before the lodgers moved in, then they likely are not TENANTS covered by the Residential Tenancies Act. Rather they are licensees and your brother has much more leeway in terminating them.  Please see our fact sheet on such matters at https://landlordselfhelp.com/media/2024-Sharing-Kitchen_Bathroom.pdf. Otherwise, the termination options are more complicated and the forms must be done correctly.