Please find below link to UK Home Office website regarding Transfer your visa to a new passport. It is not a MUST to transfer your ILR to new passport, you can carry both passports when you travelling - Please see below.
PS. Should you decide to transfer the visa to your new passport, you DON'T need a lawyer, all you need is to complete Form NTL which can be downloaded from Home Office website, attach documents that are required eg your old passport, two recent passport-sized photographs and Evidence of residence. Postal application will cost £165 and Premium application will cost £515
http://www.bia.homeoffice.gov.uk/ukresidency/transfervisatopassport/
You can choose not to have the residence permit transferred to your new passport. In that case, you should carry both your old passport and your new passport when you travel to the United Kingdom, as evidence of your resident status. If you cannot produce your original permit, you may not be allowed to enter the country.
If you do want us to to transfer your residence permit to your new passport, we cannot do this at passport control when you enter the United Kingdom. As long as you can prove that you are entitled to live here, the immigration officer at your port of entry will put a date stamp in your new passport. You must then send us an applicatin form asking us to place a residence permit in your new passport. You must be in the United Kingdom when you apply to us.