The trust's management team at Ignis Asset Management said they secured an average return of 7.7% a year on the building, which is leased to HSBC bank.
But they decided to sell the property, which the trust had owned since July 2010, because they want to reduce the £1 billion fund's holdings of under- pressure high street retail properties and boost the income yield from its portfolio.
David Rodger, one of the managers on the trust, said: "In tough markets, you have to work harder to get the returns from property."
He added: "Buchanan Street was one of the smallest assets by value in the company and one of the lowest yielding."
After the sale of 2-8 Buchanan Street to the Cordea Savills European Retail Fund, which is largely backed by German institutional investors, UKCPT now has just one property in Scotland, on Edinburgh's George Street.
Mr Rodger said there was strong demand for the Glasgow property.
"This is a landmark building on Buchanan Street," he said.
The sale was completed less than 12 weeks after it was first put on the market.
This is despite the constitution of the Cordea Savills fund having to be changed in order to allow it to invest in the property because it was previously forbidden from buying a bank building.
There are 12 years remaining on HSBC's lease. The upper floors of the building are currently unoccupied, giving the new owner the potential for development.
Mr Rodger said the Buchanan Street area was continuing to prosper, with the development of the Buchanan Quarter by Land Securities, which is due to be completed this summer.
Meanwhile, Buchanan Galleries is seeking outline planning permission for a £300m extension.
Mr Rodger noted that the Buchanan Galleries scheme features leisure facilities such as restaurants and a cinema. This chimes with the UKCPT's view that UK-wide leisure facilities are likely to be a relatively lucrative part of the property market.
The trust is being adjusted to focus more on the leisure sector and away from the high street, where spending is under pressure because of the squeeze on consumer incomes from muted wage growth.
One typical investment is the Rotunda in Kingston upon Thames on the outskirts of London UKCPT bought 18 months ago and which features a cinema and restaurants.
"The leisure sector is quite buoyant," Mr Rodger said. "Families are enjoying a trip to the cinema rather than spending the money in the shops."
Meanwhile, he noted that pressure remains on the high street, with a number of retailers going into administration in recent weeks.
But he signalled there is unlikely to be a notable upturn in the property sector outside of London in the near future.
"We think that rents are trending flat. There is little rental growth in the regions. We need to work hard to maintain income levels," he said.
UKCPT's Edinburgh property includes tenants Waterstones book shop, insurer Aviva and the Edinburgh Solicitors' Property Centre.