It is possible to use the Ordnance Survey Open Data 1 to 250,000 raster maps as a background layer in JOSM. However, the positional accuracy of this scale of map is limited. This could also apply to the StreetView tiles, but they are readily available as a WMS layer, which is probably preferable.
The OS tiles are in the OSGB co-ordinate system, but OSMuses WGS84. However, there is a plugin that can fix this, and re-project the tiles in the correct location.
Firstly you need to register and download the tiles from the OS, if you do not have access to them. This is free, but can take a while. Once you have saved these to your computer, move the TFW world files from georeferencing files/TFW/ into the main folder with the TIF images.
Then install the Import Image Plugin for JOSM, and restart as required.
To import a tile, select ‘Import image’ from the file menu; browse to and select the required TIF image (with the TFWfile in the same folder). This should be imported to the default reference system (which will be wrong, but that is changed later).
Once the image is imported, right click it in the Layers panel, select ‘Layer Properties’ then the ‘Source Reference System’ tab. Type EPSG:27700 in the search field, which should give “OSGB 1936 / British National Grid [ESPG:27700]”. You will probably want to ‘Set as Default’ so that this step doesn’t need to be repeated. But you also need to click ‘Apply Default’ at the top to re-project the image, this isn’t done when setting the default.
This should give the OS 250k raster tiles as a background layer, in the correct location with standard OSM data. Additional tiles have to be imported as separate layers, and need to be toggled when tracing at boundaries, because the images have been rotated and scaled as part of the re-projection.
Addenda This should also work for any other image map using UK National Grid, where you have (or can create) the appropriate world file for the extents of the map.