Summary: If you believe you’ve paid too much Stamp Duty Land Tax (SDLT), you can apply for a refund. To speed things up, HMRC might pay the refund before checking if you’re really eligible. However, within 9 months, they may review your case and if they find the refund wasn’t due, you’ll have to pay it back, plus any interest. If you’ve made a mistake in your claim, there could be extra penalties too. If HMRC asks for the refund back, you can either dispute their decision or accept it and repay the money. If you choose to repay, you’ll owe the refunded amount plus interest, calculated based on the time the money was in your possession.

This text is taken from the UK government guidance on stamp duty returns
“How to apply for a refund. If you think you’ve overpaid SDLT, you can apply for a refund.
To process refunds quickly, HMRC will ordinarily make the payment without checking eligibility. We reserve the right not to do so for revenue protection reasons.
This means that even after a repayment has been made, we have not agreed that the refund is due. We have up to 9 months to make a compliance check on your amended return or claim.
If you receive a repayment where the amount you claimed was not due, you must pay it back along with any interest due. If penalties apply, you must also pay them. Read more about penalties.”
Ref: https://www.gov.uk/guidance/stamp-duty-land-tax-online-and-paper-returns

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Our comment: 

Applying for a Refund: The process begins when you, as a taxpayer, identify that you may have overpaid your Stamp Duty Land Tax (SDLT). This could be due to a variety of factors such as a miscalculation, misunderstanding of the tax law, or an error in the transaction value. If this happens, you have the option to apply for a refund from HMRC. The application procedure typically involves providing details about the transaction, the amount paid, and the reasons why you believe there was an overpayment.

Immediate Refund: To expedite the refund process, HMRC may choose to issue a refund without initially checking the validity of the claim. This is done to streamline the process and reduce waiting times for taxpayers. However, it’s important to understand that this immediate repayment does not mean HMRC agrees with the reasons provided for the overpayment. They clearly state that for reasons related to protecting revenue, they may choose to conduct checks before issuing a refund.

Post-Payment Compliance Check: Once a refund has been issued, HMRC reserves the right to carry out a compliance check on your amended return or claim. This involves a detailed review of the information you provided in your refund application to ensure its accuracy and validity. It’s worth noting that they have up to 9 months to initiate this check, which means that even if you’ve received a refund, there’s still a possibility that HMRC might review the circumstances of your case. See our comment on HMRC compliance checks.

Repaying Erroneous Refunds: If HMRC, after performing a compliance check, determines that the refund was not due, you will be required to pay back the refunded amount. In addition to the principal amount, you will also have to pay any interest that has accrued on the refunded amount since it was paid to you. Furthermore, if there were any penalties associated with the incorrect claim (for example, if the error in the original SDLT return was due to carelessness or deliberate false information), you will be required to pay those as well. The exact amount of penalties can vary, and more information about them can be found in specific HMRC guidance.

If HMRC query your claim for a stamp duty refund, you will have 2 choices:

• contest their demand to return at the stamp duty refunded to you
• accept their demand and repay them.

If you repay HMRC, you will need to repay the sum paid to you and interest due. The calculation would be the sum repaid multiplied by the interest chargeable ( as of writing, 3.5% ) multiplied by the period in which the money has been refunded to you. See HMRC interest rates here.
An example: 
Principal amount (stamp duty refund) = £5000
Interest rate = 3.5% (converted to decimal form as 0.035)
Time = 8 months (converted to years as 8/12 = 0.67 years)
Using the formula, the interest payable would be:
Interest = £5000 * 0.035 * 0.67 = £117.25 (rounded to the nearest penny)

In essence, while HMRC tries to expedite the refund process, it maintains the right to verify the validity of refund claims and recover any wrongfully claimed amounts, along with any applicable interest and penalties.