The hacking group Anonymous is alleged to have disrupted access to the Home Office website, apparently in protest at government policies.
The website became inaccessible around 21:00 BST on Saturday, and service was patchy from 05:00 on Sunday
An Anonymous Twitter message warned of the attack on 4 April.
One message on Twitter said it was a protest against "draconian surveillance proposals" but another claimed it was over extradition from the UK to the US.
There were also claims on Twitter that the 10 Downing Street website had been targeted as part of the same protest.
This was dismissed by a Downing Street spokesman - but access to Number 10's site was slow and intermittent for a time.
It is not clear whether the protest was against email surveillance or extradition, but it could be both.
One tweet claiming to be from Anonymous said: "You should not give UK citizens to foreign countries without evidence. If an offence happened in the UK, so should the trial."
Last month the Commons Home Affairs Select Committee said major changes were needed to the UK-US extradition treaty to restore "public faith".
The MPs said they believed it was "easier to extradite a British citizen to the USA than vice versa".
Earlier in the week the Home Office said it planned to "legislate as soon as parliamentary time allows" to bring in email surveillance measures.
Ministers say change is needed to help fight crime and terrorism, but critics warn it is an attack on privacy.
After the website was disrupted on Saturday evening a Home Office spokesman said: "We are aware of some reports that the Home Office website may be the subject of an online protest.
"We have put all potential measures in place and will be monitoring the situation very closely."
"If a successful denial of service attempt does occur tonight, we will liaise with the technical team and update as necessary," he added.
Anonymous is a loose group of "hacktivists" who came to the fore in 2010 in the wake of the emergence of Julian Assange's Wikileaks website.
Anonymous began by aiming distributed denial-of-service (DDoS) attacks on websites, like the credit card firm Visa, who had withdrawn services from Wikileaks.
But it has gradually changed into a grouping which claims to battle government surveillance and attempts to police the internet.
Earlier this week Anonymous claimed to have defaced almost 500 websites in China.
A message put on the hacked sites said the attack was carried out to protest against the Chinese government's strict control of its citizens.