The Markit/CIPS purchasing managers' index (PMI) for the sector moved up to 52.6 from 52.3 in September.
IHS Markit's senior economist Tim Moore said the news was "positive".
But he warned that "respondents noted that Brexit-related uncertainty and concerns about the UK economic outlook had held back investment spending".
He added: "While business activity has picked up since the third quarter, the recent phase of new order growth has been the weakest for three-and-a-half years.
"Subdued new order intakes contributed to a fall in construction sector business confidence for the first time since July."
Markets analyst Neil Wilson said: "The market is holding up very well since the [Brexit] vote.
"Residential housing activity was the key driver and this confirms that in terms of the fundamentals of the UK housing market, nothing has really changed.
"The market remains undersupplied and with interest rates at record lows, there is no reason for buyers not to be found.
"Even if prices are pressured and household incomes are constrained by inflation, at the first-time buyer level there is no lack of demand."
However, the figures are at odds with last week's GDP figures, which said that the construction sector had contracted by 1.4% in the three months following the Brexit vote.
While construction rose according to the survey, figures for commercial construction stabilised during the month, but civil engineering decreased slightly.
There was only a moderate growth in new business in October and the increase was much weaker than in the first quarter of the year.
And input prices increased at the second-fastest rate since July 2011.
Reports suggest this is because of suppliers trying to pass on higher prices for imported raw materials following the decline in the value of sterling in the wake of the Brexit vote.
On Tuesday, the Markit/CIPS survey on manufacturing for October showed it remained on a "firm footing" during the month.
And later this week, the Bank of England meets for its latest policymaking meeting, although it is not expected to announce another cut in interest rates.
UK construction companies enjoyed a rise in business activity in October, largely thanks to another big increase in residential work, says a survey.