Most councils will not allow a plaque to be added to a street tree. Councils are very resource poor, and the extra task of adding a plaque to a tree is simply not practical.
In some cases, if your council runs a dedicated memorial tree planting programme, then they may have a process in place to arrange for a plaque. These memorial programmes tend to be restricted to more high-profile locations, such as parks and town squares, and often the locations will have been pre-selected by the council.
Head over to your council’s page to find out what they offer.