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Independent MPs

At the beginning of the 2017 parliament, there is one independent MP:
Lady Hermon, formerly UUP, MP for Down North.

At the end of the 2015-17 parliament, there were five independent MPs. Their names (with wiki links for now are):
Simon Danczuk, formerly Labour
Lady Hermon, formerly UUP
Natalie McGarry, formerly SNP
Michelle Thomson, formerly SNP.
and Douglas Carswell left UKIP to become an independant on 25th March 2017. Much to UKIP's annoyance, he does not intend to trigger a by-election.

Sources
Wikipedia.