As a long-term investor, I aim to buy UK shares I can then hold for decades, in some cases barely thinking about them as they tick over in the background.

In practice, things may not always go so smoothly. Situations can change and a once-great business can suddenly run into problems.

But I continue to scour the UK stock market for shares I could buy with the intention of holding them for the long term.

Here are three that have caught my eye.

Diageo

I am in a dilemma about my existing shareholding in drinks company Diageo (LSE: DGE).

The Diageo share price has been sinking and is a quarter below where it stood a year ago.

I have no plans to sell my shares. I reckon the massively profitable firm with its unique portfolio of premium brands such as Guinness and Smirnoff has strong long-term prospects. Its share price drop seems overdone to me.

But here is my dilemma. Do I buy more?

So far, I have held off. Supply chain problems have dented my confidence in management, while weaker demand in key markets is a short-term risk to add to the long-term challenge of younger consumers drinking less alcohol.

But if I do not see the current share price as a bargain, should I just cut my losses altogether?

On balance, although I am not currently adding to my shareholding, I reckon Diageo could well merit a place in my portfolio for decades.

British American Tobacco

There is another FTSE 100 firm in an industry that attracts opprobrium that I do not plan to buy soon: British American Tobacco (LSE: BATS).

Here, my reasoning is different.

Over time, cigarette sales are likely to keep falling. That is already posing a challenge to the Lucky Strike maker’s sales volumes and profitability.

But it has been happening for decades already – and still British American powers on. Like Diageo, it has raised its dividend per share annually for decades. Dividends are never guaranteed, but the current yield of 7.2% does tempt me to add British American back into my portfolio.

However, with its large debt pile and ongoing challenges of falling cigarette use, the current share price is too rich for me.

If it comes down to a level I see as attractive, I will add it back to my portfolio.

Judges Scientific

Price is also the reason I am not currently planning to buy back a former holding, Judges Scientific (LSE: JDG). At the right price, though, I would – so it is on my watchlist.

Unlike the well-known UK shares above, Judges with its £541m market capitalization probably flies beneath many investors’ radar.

But it has been a standout performer, moving up 88% in five years and with a run of annual double-digit percentage increases in its dividend per share to boot.

What I like about Judges is its business model. It buys up small and medium-sized precision manufacturers of specialist scientific instruments. That is an industry with ongoing demand where quality matters, meaning customers are willing to pay a high price.

There are risks: Chinese order intake remains weaker than before and last year saw overall revenues fall.

The current price-to-earnings ratio of 52 is too high for me, but if the valuation becomes attractive enough I will buy.