This shows the whole of Toxteth Park as defined in the 1765 map of the Earl of Sefton, probably produced for the Enclosure Act.  

The Upper Brook and Lower Brook are both shown, but as the origins of both fell outside of the Park, then it has not been possible to trace these accurately in their upper reaches.

Parliament Street
Smithdown Road
Greenbank Road, Penny Lane, Ibbotsons Lane
Lodge Lane
Ullet Road
Park Road/ Aigburth Road

 
The Upper Brook rose somewhere near Sandown Road in Wavertree and seems to have flowed across what is now Wavetree playground, reaching Smithdown Road to the east of the Brook House Hotel and just to the east of Lidderdale Road. Recent examination of a building site adjacent to the Brook House car park shows no trace of the stream where Robert Griffiths reported it flowing above the surface in 1908.
However at the edge of the pub car park (town side) there is a wooded, grassy bank below which are the sides of a rubbish-filled ditch.  In places this is remarkably deep despite its tin and plastic overburden. This ditch begins just where the culverted stream is shown on the 1905 map, at the end of Foxdale Road and then follows the edge of the car park becoming deeper towards Smithdown Road where it was some 6 feet below the surface of the adjacent bank. This is probably a redirection of the flow of the original stream.  Visualising the line across Smithdown Road shows that IF this were the bed of the Upper Brook then it would re-appear on the far side, behind the garage and run in a line behind this, initially along the boundary with St Columbas Church.  There is a ditch or embankment marked on the 1905 map of the area. This is speculative but beyond a doubt there is a ditch there and in places this is both deep and wide. It is where the stream should be on the map and this is also the lowest part of this portion of Smithdown Road - and streams do not flow uphill.

Having crossed Smithdown Road Upper Brook continued parallel to what is now Greenbank Road, and subsequently what was left of its flow (for the historical upper reaches were severed by a railway line - the Liverpool and Garston branch) dropped, at the end of Gorseland Road, opposite Elmbank Road, into a lake formed by its damming in Greenbank Park. It can still be seen there within Greenbank Park.

From there its drainage continues more or less due south until it suddenly appears to veer west, in the region of Ibbotson's Lane, where a tiny above-ground fragment is still visible, emerging at The Dell in Sefton Park, near the end of Queen's Drive. You can stand on the Iron Bridge which spans The Dell and look up a shallow, wide, wet valley with a the brook discharging out of a drain. It is not picturesque, and the trudge 'upstream' is a soggy but uninspiring one, but it's historical and part of the river systems of toxteth!

Finally the stream is found flowing due west throught The Dell and into the main boating lake at Sefton Park where it joins the waters of the Lower Brook.