There are a large number of roses that fit perfectly with the Tudor rose description... white centers with red rimmed edges. For example, the lovely Double Delight.
The first time it was unveiled was with the marriage of the House of Lancaster's Henry VI to Elizabeth of York. This symbol was the start of the Tudor dynasty which lasted well over a hundred years. It was used in widespread official goverment documents, house decorations, and as official insignia of the Tudors.
You may see this symbol hidden in other English insignia. It sometimes can be combined together with other symbols, as can happen over time. You'll also see slight variations in the backing leaves. Some may have the green leaves with a stem, some may not.
Today, the Tudor rose is not used in most official English business. However, you'll still see it on some government workers, such as some of the groundskeepers at the Tower of London. Members of the Tourist Board and the Supreme Court also were this as a badge on their uniforms. The rose itself is still a strong symbol in England, with many pubs being named after the rose.
But you will still see plenty of references to the old red and white symbols of Lancaster and York in those areas of the country. I guess old rivalries die hard.