I'm not in the UK but I can deduct some clothing items as business expenses entirely if they meet certain criteria (need to be bought as considered an essential part of the job -specifically to meet safety standards- and would not buy them or use them outside of work otherwise). If my business was in the line of a fashion blogger's at the very least I could deduct the VAT and if you got creative with it you could probably still deduct it in part (basically arguing it complied to the primary criteria for editorial or personal brand building, then selling the item from your business to your person at a fair market rate, which is very far away from RRP in handbag land). Was there mention of where the bag was bought? I remember a few years back Selfridges would hand out very generous gift cards that incited many designer handbag buys.
Loewe does give away freebies but more on the celebrity level with those who have an influence on fashion/trends (think Kate Bosworth and similar). They probably gift to the upper tier of fashion bloggers as well as the puzzle bag and the elephant one were all over Instagram in late 2015, early 2016. It's ruined what is otherwise a lovely brand with quality bags for me, their pricing is also insane, it's highly overpriced in recent times and then with the exception of the very popular models in specific colours, they slash the prices heavily in sales (I've seen up to 70%). They're presented as investment bags on SM but they drop in price instantly once you walk out the door with them. See also, J.W. Anderson (who happens to design for Loewe), Marni, and many many others. Chloe is a notable repeat offender by constantly pushing a new 'it' bag like it's fast fashion, they are so obviously designed for Instagram.
Zara famously has a very minimal PR budget, I've never seen them actively work with influencers but it doesn't mean it doesn't happen. That goes for all their other brands too (Massimo Dutti, Oysho, Stradivarius, Bershka, etc). COS also has very specific PR strategy that eschews mainstream SM, they sponsor and curate installations at art and design events instead. &Other Stories also appears to be very selective and H&M only seems to work in specific campaigns, eg. when their new and improved beauty line launched they utilised some bloggers.