Officers have suggested the suspect, who has targeted five properties in the well-to-do areas of Kensington and Holland Park could be a scaffolder or builder, with the ability to scale walls and climb roofs and drainpipes during break-ins - writes itv.com
One victim, who had a diamond engagement ring and a vintage watch belonging to her late mother stolen, has offered a reward of up to £40,000 for their return.
In a statement released through the Metropolitan Police, the victim said: "The fact that someone came into my house uninvited and rifled through my possessions is distressing.
"The items which were stolen were of huge sentimental value as they belonged to my late mother. She wore the ring and watch every day and they have been in our family for more than 70 years."
Police have released CCTV of a man they want to speak to, who is seen searching a property with a torch on an evening in March. Officers said children were in the bath in the next room at the time.
Detective Constable Eve Kelly appealed for anyone with information about the break-ins, which happened between March 3 and April 21, to contact Kensington and Chelsea police.
She said: "The value of the property stolen amounts to hundreds of thousands of pounds and includes items of highly sentimental value which are irreplaceable.
"This type of crime has a huge impact on not only the victims and their families, who no longer feel safe in their own homes, but upon the local community who are worried he will strike again. This man must be arrested."
Scotland Yard described the suspect as white, aged between 20 and 40, with an athletic build, a shaved head and facial stubble.
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