The FTSE 100 was down 0.3 percent, ending a six-day winning streak, and the FTSE 250 was 0.2 percent higher by 0937 GMT.
BP, which had led the main index higher with a more than 5 percent gain on Tuesday after strong results, dipped along with other oil stocks as crude prices fell. A stronger pound and Clydesdale Bank owner CYBG's upbeat quarterly report boosted the mid-cap index.
Trump's renewal of a demand for $5.7 billion in funding to build a US-Mexico border wall stoked fears of another US government shutdown, helping keep Asian stock markets subdued overnight.
However, London Capital Group analyst Jasper Lawler said there was nothing "too shocking to cause any kind of risk aversion in the address".
"What we are seeing is just a little bit of weakness giving back some of those gains... more like profit-taking than any new contributing factor."
Online retailer Ocado slumped 8 percent and was on track for its worst day in more than five months after it said a fire at its automated distribution centre in Andover could hit sales growth.
Investors also sold off UK financial stocks after France's largest listed bank, BNP Paribas, cut its 2020, targets. GlaxoSmithKline was 1.6 percent lower ahead of its full-year results later on Wednesday.
Midcap CYBG, a newly emerged challenger to Britain's big retail banks, surged 14 percent - its best intra-day gain ever - after reporting a rise in first quarter lending.
Markets are awaiting the Bank of England (BoE) meeting on Thursday where Governor Mark Carney and his fellow interest rate-setters are expected to keep borrowing costs on hold.
"What you want to see is an acknowledgement from the BoE that actually wage pressures are growing, inflation is at or above target, and so if and when Brexit uncertainty diminishes or disappears then they are ready to start tightening policy," Lawler said.
"But I suspect we're probably not going to get that ... Bank of England doesn't want to signal any kind of tighter policy while Brexit is still in full flux."
Irish building materials group CRH gained 3.3 percent and outperformed the main index after a Reuters report that activist investor Cevian Capital had built a stake in the group.
Britain's biggest housebuilder Barratt rose 3 percent after it posted higher first-half volumes and, in relation to Brexit, said it was working with suppliers to ensure continuity of supply of overseas components. Peers Berkeley and Persimmon also rose.
The Telegraph reported late on Tuesday that UK cabinet ministers had secretly held talks on plans to delay Brexit by eight weeks, potentially postponing Britain's exit from the bloc to May 24.
Small-cap support services provider Interserve surged 10 percent after striking a deal with creditors to more than halve its debt by issuing new shares.