The cooling-off period for an online order has been extended to 14 calendar days from seven working days.
Shoppers can claim a full refund during this period without having to give a reason for the cancellation.
Companies must also offer phone lines that cost no more than a local call for customer inquiries or complaints.
The rules see the final stage of implementation of the EU Consumer Rights Directive.
The regulations cover a number of areas of consumer rights, including the introduction of a cooling-off period for digital music, films and books for the first time.
Retailers must not supply the content within the 14-day cancellation period unless the consumer has given their express consent to this happening, and the consumer must also acknowledge that once the download starts they will lose their right to cancel.
Any extra charges for those buying with a debit or credit card must be clear from the start, the rules state.
The rules should bring an end to calls that can cost up to 41p a minute, for those trying to make a complaint.
Companies will still be able to use phone numbers that carry higher charge rates when customers are purchasing goods or services, but not when they call afterwards to raise questions or complaints about them.

Two men found the victim lying on Hope Street, near to Argyle Street, at about 04:30 on Friday 19 February.
The man was treated in hospital for a head injury and released. He was re-admitted at a later date and told he needed surgery for a fractured skull.
The incident was reported to police on 3 March. They want to trace the two men who found the man and other witnesses.
Det Con Stephen Palmer said: "A man has been left with a very serious head injury as a result of this attack and inquiries are at an early stage to establish what happened.
"I would like to speak to anyone with information about this incident, particularly the two people who called an ambulance for the victim."
Online shoppers now have longer to cancel orders while complaints calls should be cheaper, under laws that take effect on Friday.
[NEXT_CONCEPT]
A man found lying in the street in Glasgow had suffered a fractured skull after being attacked, police have said.