First, here's the Google Earth view across the railway towards my street. South is at the top, the A40 Westway (elevated road) is at the bottom, Royal Oak station is on the left in the middle of the bridge, and Paddington Station is about a half mile beyond that:
The strip of land containing the railway and the construction site etc. is about 70 metres N-S according to Google Earth.
The satellite picture is several years out of date - the old tracks nearest the bottom, which used to be part of the goods lines into Paddington and its shunting yard, have now been removed, and that's where the Crossrail construction is now happening. South of that are the two tracks of the Hammersmith and City line, currently closed for refurbishment, which go into a cutting to the right of the picture, then the four main electrified lines into Paddington station, then furthest South two more lines that aren't electrified - I don't think they're used any more, I'm pretty sure that even the steam trains going into Paddington now run on the electrified lines.
The cutting leading to the Crossrail tunnel is going to start roughly in the middle of the picture, between the Hammersmith and City line and the Westway. This annotated map may make it clearer - the Crossrail line starts going down into the ground, going off to the Left, with the "crossrail portal", the actual tunnel entrance, just before Royal Oak station. I've indicated the approximate position, but I may not have it exactly right. It dives underground and will eventually connect to Paddington Station via new underground platforms. My house is just to the right of the yellow arrow.
Because of all the trees in the way it's difficult to take pictures from my side of the railway that show what's going on - here are a couple I took from my front steps.
I took some pictures from the North side of the railway under the Westway, where there are some openings in the wall giving a view out onto the tracks, but the steel grid covering the opening is narrower than the camera lens, so I wasn't able to take an unobstructed shot.
This is a machine that's been putting in some steel shuttering between the Crossrail construction site and the Hammersmith and City Line (which is also the Circle Line to Hammersmith). There's going to be a deep concrete barrier between the two lines, so that the eventual excavation of the Crossrail cutting won't cause the land under the H&C line to collapse. At the moment the shuttering is a couple of metres high, I'm not sure if they plan to leave it that height. I hope not, because it isn't very attractive and it'll spoil the eventual view of the trains. There are five or six other machines, cranes and so forth, but none of them was in a good position for photos today.
Finally, this is one of the construction machines on the Hammersmith and City line.
Eventually the giant Crossrail tunnelling machine of doom will arrive and vast quantities of excavated material will be transported across this area and out. I think that they're using the railway for that but I could be wrong.
Lots more about Crossrail on Wikipedia:
I'll try to post more updates as it continues.