According to the CRAs, only the company that performed the searches can authorise removal of them so the first step will be to write to the company and ask nicely (but firmly) that they either remove the search records or provide evidence of their right to perform the search.
Be aware that writing to the company could 'open a can of worms' (but so can checking your credit file) as lots of people crawl out of the woodwork claiming for debts that are not yours but someone with a similar name and date of birth.
If you're not planning on applying for credit any time soon, it may not be worth it because they should disappear after 12 months anyway.
I am not an expert in law, finance or any related field, I just read a lot. Any advice is based solely on what I've read so please don't take it as gospel without checking it out yourself.
I prefer not to give advice by PM. If you want me to look at something, send me a link to your thread, and if I can help I'll reply on there.