Sadly the ASA only deal with actual adverts rather than gifts. Basically the company needs to have some sort of control over the material for it to be considered an ad. Now some gifts will be ads if an influencer is stupid enough not to negotiate proper payment and is accepting the gift in return for specific content, but that's the general rules. Influencers should be declaring gifts though, I believe the CMA cover it, but the ASA only respond and investigate if it is definitely an advert. I am not entirely sure if you can report directly to the CMA though.
If the sofa woman is repeatedly gifting with such high value items, you do have to question where that line is though, especially if she is gifting KNOWING that they will be shared versus someone sending something and just hoping it may feature at some point.