The latest figure comes after Foreign Secretary Philip Hammond warned that it was highly likely a “significant number” of victims yet to be identified would be British.
A total of 38 people were killed when gunman Seifeddine Rezgui opened fire on a beach in the Sousse resort on Friday, with the the Foreign Office already confirming 15 of them were from Britain.
At a briefing following an emergency meeting of cobra, Home Secretary Theresa May also said the British deaths figure was expected to rise as more information comes out.
Three Irish people are also among the dead.
Mr Hammond said there had been delays in identifying victims because many were “dressed for the beach, not carrying ID physically on them”.
He added: “There are a significant number of victims who have not been positively identified at this time and it is highly likely that a significant proportion of them will be British.”
He said it was “extraordinarily difficult” to predict where the next attack will happen and was no more likely to be in Tunisia than in a European city.
“Our agencies have been very frank about this over a long period of time now, they cannot guarantee that we will be safe from this kind of self-radicalising lone-wolf attack. It is the most difficult type of attack to detect and predict and therefore the most difficult kind to protect against.”
Investigators have revealed they are looking for at least one more accomplice, with an Interior Ministry spokesman in Tunisia telling the Associated Press they are sure that Rezgui had help.
Mrs May said earlier today there was no evidence that Rezgui had chosen the Sousse resort because of the high number of Britons that flock to the popular holiday destination.
But the terror threat Britain is facing is becoming more diverse with a possibility of more spontaneous lone wolf attacks attacks, she added.
Over the last decade about 40 terror plots are believed to have been foiled by the security services.
Asked if the beach had been targeted because of the high number of British tourists using it, she replied: “This is still ongoing investigations and we are working very closely with the Tunisian authorities in relation to this.
“I’ve seen no evidence so far that this was targeted because there are British tourists there, but, of course we must recognise this is the most significant loss of life in a terrorist attacks since 7/7.”
Asked about reports that four major plots in London in the last few months have been halted, Mrs May said: “Yes, a number of plots have been stopped.
“Over the last ten years it’s estimated that something like 40 plots have been disrupted here in the UK.
“The threat has become more diverse over time. It has changed over time. That’s why it’s important for us to sustain the counter-terrorism capabilities of the agencies.
“We see that you have not just those who will plot for some time, perhaps in a group to undertake a complex attack, but also the possibility of more spontaneous attacks, these so-called lone wolf attacks.”
Mrs May said the government will be introducing a counter-extremism strategy to tackle radicalisation.
Since December 2013 more than 70,000 pieces of extremist material have been removed from the internet, she added.
Mrs May said: “We want to work with families and communities so if they are seeing signs of somebody being radicalised, if they are concerned about the behaviour perhaps of their son or daughter or perhaps of somebody’s friend that they are actually able to come forward to the authorities and talk to us about this so we can perhaps stop somebody from going down that path of radicalisation.”