Penny Mordaunt lost in Portsmouth North while Tobias Ellwood also lost his Bournemouth East seat.
The Home Office reportedly hopes to house 500 people on the Bibby Stockholm off Portland, in Dorset.
The government hopes new centres for asylum seekers will cut down on the use of private hotels.
Richard Drax is facing demands to pay compensation for the role of his ancestors in the slave trade.
A group of about 40 people walked on to Richard Drax's land to "start a conversation" about access.
Graffiti reading "Slaver" and "BLM" was daubed on the Drax Arms in Bere Regis Dorset overnight.
