The following has just been extracted from Timatic via EF. The bolded provision seems to be most likely to be the one applicable. Is that the kind of Schengen visa that they have?
Visa, Health & Passport:
United Kingdom - Transit Visa
Visa required.
Visa Exemptions
Passengers with a Hong Kong (SAR China) passport for a maximum stay of 6 months.
Passengers with a Macao (SAR China) passport for a maximum stay of 6 months.
Passengers with one of the following documents issued by the United Kingdom:
- an EU Settlement Scheme (EUSS) Family permit; or
- a Jersey, Guernsey or Isle of Man Settlement Scheme Family Permit; or
- a settled or pre-settled status under the EU Settlement Scheme (EUSS); or
- a settled or pre-settled status under the Jersey, Guernsey or Isle of Man Settlement Scheme; or
- an application for EU Settlement Scheme (EUSS); or
- an application for Jersey, Guernsey or Isle of Man Settlement Scheme; or
- a Service Provider from Switzerland visa if they are a Swiss national.
TWOV (Transit Without Visa)
Nationals of China (People's Rep.) with a normal passport transiting through London (LHR) or Manchester (MAN) with a confirmed onward ticket for a flight to a third country on the same calendar day. They must:
- have a visa issued by Australia, Canada, New Zealand or USA, and
- stay in the international transit area of the airport, and
- have documents required for the next destination.
Nationals of China (People's Rep.) with a normal passport transiting through London (LHR) or Manchester (MAN) with a confirmed onward ticket for a flight to a third country on the same calendar day. They must:
- have a "C" visa issued by Ireland (Rep.) with the remark: "BC BIVS", and
- stay in the international transit area of the airport, and
- have documents required for the next destination
Nationals of China (People's Rep.) with a normal passport transiting through London (LHR) or Manchester (MAN) with a confirmed onward ticket for a flight to a third country on the same calendar day. They must:
- have Schengen "C" Approved Destination Scheme Group Tourism Visa issued by a Schengen Member State with ADS or SDA noted in Remarks, and
- be arriving from the Schengen Member State that issued the visa, and
- have stayed in the Schengen area for a maximum of 30 days, and
- stay in the international transit area of the airport, and
- have documents required for the next destination.
Warning: Transit through the international transit area of Manchester (MAN) is possible between 5:00 and 21:00 on the same calendar day.
Additional Information
Passengers with an indefinite leave to remain in the form of wet ink stamps issued by Guernsey, Isle of Man or Jersey can enter or transit through the United Kingdom. They must not have stayed outside Guernsey, Ireland (Rep.), Isle of Man, Jersey or United Kingdom for 2 years or more.
Warning
E-visas are accepted for airside transit if the airline verifies it with the issuing country.
Although the language seems to permit transit on two separate tickets, there may be a separate battle to persuade check-in at BSL that they will not be leaving the "international transit area" because they don't have any checked bags.