Under British consumer law is a high-street retailer obliged to sell a
product [to the consumer] displayed in the store if it is marked with
a price,
even if the displayed product is the only one in the store?

Dear lewis10-ga,

The shop is not obliged to sell you the product. The Trading
Standards' web site gives the following information on this subject,

?Under law, a retailer is entitled to decide the price he wants to
charge for his goods. The price on display is simply what the law
calls an 'invitation to treat'. In the same way you don't have to buy
goods from anyone, a retailer is under no obligation to sell you
anything. You cannot insist that a shop sells you anything at a marked
price, whether or not they have made a mistake.?
http://www.tradingstandards.gov.uk/cgi-bin/calitem.cgi?file=ADV1011-1111.txt

How is the contract made?
"When a trader displays or advertises goods or services, he/she is
giving consumers what is referred to as an ?invitation to treat?. The
consumer will then make an offer to buy the goods or services, and at
this point the trader is under no obligation to accept the offer. A
contract is made if and when the trader accepts the offer."
http://www.tradingstandards.gov.uk/cgi-bin/bglitem.cgi?file=badv073-0100.txt


The same applies in Scotland. 
Dundee City - trading standards advice.
"I saw goods marked at a low price in a shop but the shop refused to
sell them to me. Can they do this?

Yes. A shop is not bound to sell you anything or at any price on
display. They are making an invitation to treat, and the invitation
can be withdrawn at any time. It is the buyer who makes the offer to
buy. However, price indications should not be misleading. If they are,
it could be an offence under the Consumer Protection Act 1987 and
should be reported to your local Trading Standards Office."
http://www.dundeecity.gov.uk/ehts/questions.htm


This practical example from a case involving Argos may help. The first
part of the article deals with the offering of the item. The second
part (not copied here) discusses a possible offence of showing a
misleading price which is not applicable to your example.)

?A shopkeeper has a television for sale. He puts it in the window with
a large sign advertising the price. A customer sees it in the shop
window and offers to buy it. The shopkeeper does not have to sell the
television if he does not want to. At that stage there is no contract.
The shopkeeper is making what lawyers call an 'invitation to treat',
an invitation to the customer to make him an offer. So the customer
cannot insist on buying the television at the advertised price. If the
shopkeeper has put an unusually low price on it - deliberately or by
mistake - he can refuse to do a deal with the customer.?
http://news.bbc.co.uk/1/hi/business/the_economy/441740.stm

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder

Search strategy
trading standards uk
"invitation to treat" price shop

Does this strike anyone (outside of the US) as vaguely unfair?

Mark,
Yes, in Germany goods have to be sold as advertised, and a store or
chain can't just have one or two bargain priced items if they put an
ad it the papers.
A demonstrably misspriced item excepted.

But the English Common Law solution is tried and tested.  One just has
to understand it.