Clarification questions:
Are we looking for the UK marketshare vs the Global market?  Yes
What type of art should we focus on? Abstract art, fine art, local artist art? All art
What time frame are we talking about? 1 year

Calculation: (UK Sales/Global Sales)*100 = UK Marketshare

Assumptions:
Global Population: 7.7B = ~7B = average household (HH) of 4 = ~1.75B
UK Population: 66M = ~60M= average household (HH) of 4 = ~15M

Next is to figure out how many HH buy art global vs UK:
When looking at Global population- out of 195 countries, one needs to consider affluent countries ( US, UK, China, etc) who have dispensable income to invest/buy art vs third world countries. Let’s estimate 2% of the Global population makes up the upper class that buys art globally.
2%(1.75B)= 3.5M HH who buy art

When looking at UK population – there is a higher percentage of the population that can buy art
Lets estimate 6% of UKs populations makes up upper class that buy art in the UK.
6%(15M)= 900,000 HH who buy art

For simplicity, I will use USD:
Cost of art can vary from $5 to $500K per piece but based on UK higher wages and costs and more dispensable income let’s estimate $300 is what a HH spends per year.

UK Sales: 900,000($300) = $270,000,000
Global Sales: 3,500,000($300)= $10,500,000,000

Calculation: (UK Sales/Global Sales)*100 = .02 = 2%

Sanity Check: 2% seems very low for such a high-earning country like UK which has higher cost of living/wages, therefore, higher dispensable income that they could potentially invest towards art.  It’s probably better to segment the population into elite, high income, and middle and then estimate the spend for each on art.  e.g. Elite $300,000; Upper Class $30,000; Middle Class $300.

I would re-estimate with this into consideration, the UK markeshare would increase to ~15%

We should also consider external variants in the market that could impact purchases such as good economy vs COVID that would influence sales.

The real answer from Google Search:  20% = UK share of the global marketshare value in 2020.