This work outlines and assesses several methods for the detection of manoeuvres in Low Earth Orbit (LEO) from surveillance radar data. To be able to detect manoeuvres, the main starting assumption is that the object under analysis has an orbit known with a sufficient degree of precision. Based on the precise (a posteriori) orbit and radar data, several manoeuvre detection methods are presented; one is based on unscented Kalman filtering, whereas two others algorithms are based on reachability analysis of the state, which correlates its prediction set with the next track from the radar. The filtering algorithm can be extended for several radar tracks, whereas the reachability-based methods are more precise in detecting manoeuvres. Then, to inherit the best properties of both classes of algorithms, a manoeuvre detection filter that combines both concepts is finally presented. Manoeuvre detection results are presented first for simulated scenarios -- for validation and calibration purposes -- and later for real data. Radar information comes from the Spanish Space Surveillance Radar (S3TSR), with real manoeuvre information and high-quality ephemerides. The results show promise, taking into account that a single surveillance radar is the only source of data, obtaining manoeuvre detection rates of more than 50% and false positive rates of less than 10%.