Of those surveyed some 46 per cent said the prime minister had dealt with the incident well, after weeks in which she has accused Moscow of the attack and led an international coalition to expel Russian diplomats.
According to the poll by BMG Research, the same proportion also disapprove of the way that Jeremy Corbyn has handled the affair, with the Labour leader having refused to directly blame the Kremlin for the incident.
It may be because almost half of those who took part in the survey are also convinced Russia was behind the attack, according to the survey.
The poll asked respondents “how well or badly” they thought different politicians had handled the “incident in Salisbury and its aftermath” – which saw ex-Russian spy Sergei Skripal and his daughter poisoned with a novichok nerve agent.
For Ms May, 46 per cent said she had handled the situation well, with 27 per cent saying she handled it badly and 26 per cent saying that they did not know.
When it came to Mr Corbyn less than a quarter, 23 per cent, said he had handled it well, while 44 per cent said it had been handled badly and 33 per cent said they did not know.
The Labour leader can take comfort in that the public thought the foreign secretary had dealt with the situation even worse.
Some 45 per cent said Boris Johnson handled Salisbury badly, while 23 per cent said he handled it well and 32 per cent said they did not know.
The prime minister scored an international coup when she convinced the leaders of the US, France and Germany to join her in making a joint statement for the first time, condemning Russia for the attack.
She later expelled Russian diplomats from the UK, with a string of her allies including the US, France and Germany following suit.
Mr Corbyn on the other hand was plunged into party infighting when he refused to blame the Russian regime in the House of Commons for the attack, with his spokesman instead suggesting that it could have been down to criminal gangs.
But according to the BMG poll only 6 per cent of the public believed that suggestion. More people, 7 per cent, thought MI6 might be behind the attack and 33 per cent did not know.
BMG interviewed a representative sample of 1,562 adults living in Great Britain between 10 and 13 April. Data are weighted. BMG are members of the British polling council and abide by their rules