Products that may be substituted by a pharmacist without a new prescription from a doctor include some gels - Oestrogel and another called Sandrena.
Ovestin cream and a spray called Lenzetto are also on the list.
Hormone patches would be a good swap, and these are in plentiful supply.
Anyone who has questions or concerns about HRT should speak to their pharmacist or doctor, experts advise.
The Royal Pharmaceutical Society welcomed the move but said it would still like to see a permanent change in the law to make it easier for pharmacists to make swift appropriate swaps for all types of medicine - not just certain HRT products when they are in short supply.
The government says it has been looking at a variety of ways to improve supply quickly after it heard how women were experiencing distressing symptoms, because they were unable to get their choice of medication.
Madeline McTernan - the new HRT tsar whose job is to help solve the crisis - said the situation was improving.
She said: "I am very encouraged by the constructive engagement across the sector, and enthusiasm with which suppliers and pharmacists are looking to work with us to meet this challenge.
"Focusing both on measures that ensure we can use stocks most efficiently, whilst also ensuring supply is increased, is critical."
Women's health minister Maria Caulfield said manufacturers had told the government that by June "they should be in a better position [on supplies]".
She told BBC Radio 4's Today programme that of more than 70 HRT products available in the UK, "it is only about 10 where there is a struggle with supply".
She added that "we are looking at all options" when asked about making permanent the temporary powers pharmacies have to swap prescriptions.
Prof Claire Anderson, president of the Royal Pharmaceutical Society, said: "The advice on which HRT product to substitute with another has been drawn up by experts, and women can be confident they will receive what's appropriate for them.
"This short-term measure will help women access supplies of HRT medicines, which are difficult to get hold of.
"This is a very fluid situation with some products due to return to normal availability shortly."
Availability of a tablet called Premique Low Dose has improved, and there are now good stocks of it in pharmacies.
The British Menopause Society has information on choosing HRT products, as does the health advisory body the National Institute for Health and Care Excellence (NICE).
HRT is a treatment designed to relieve symptoms of the menopause. The shortage has meant some women turning to the black market.
Some pharmaceutical companies say increased demand is the main reason why some supplies have run low.
That demand is driven by a greater awareness around the menopause - thanks to campaigns - and more confidence around prescribing HRT.
Prescriptions for HRT in England have more than doubled since 2017.