The most common cause of gutters overflowing is loose roof moss being washed down into the gutters causing a blockage, either in the gutter itself, in the downpipe, or, even worse, in the underground pipework which can cost a small fortune to solve. The solution is to have it removed and then a fungicidal spray treatment applied to the tiles to help slow down re-growth.
Ideally it should be removed manually with a scraper/brush, do not take short cuts like using a pressure washer on the roof which can strip the tiles of any colour and in extreme cases actually damage the tiles. Once the moss is removed check the roof for chipped or damaged tiles and replace them, then clear out the gutters of and any blockages. Finally spray the roof tiles with a fungicidal spray treatment . This will kill off any moss spores and will prevent early re-growth as well as kill off any algae and roof litchins.
This method of removal will not invalidate most manufacturers warranties. There is no flood risk like the risk associated with using pressure washers. The method will not strip colour from the tiles thus preserving the character of the property and saving a fortune on roof coatings. Many roofing companies push their roof renovation systems such as coatings and sealants on to customers who just want a clean roof. Manual removal is a simple yet somewhat time consuming process that gives the homeowner exactly what they want - a moss free roof, reduced gutter blockages and less drop off onto lawns and gardens.