Cycle access onto roads opposite junctions

What about comparing this situation with the situation where there was a residential road coming from the new development here?

If there was a road coming from the new development, there would be no problem with having it come up to the road, surely. Intersections aren't a strange thing to have. Now, change the situation so that the same number of pedestrians and cyclists (and perhaps even a few more) use that road, but only VERY FEW motor vehicles. Surely that doesn't make it unsafe, does it? If anything, it makes things safer. Ok, now remove even those very few motor vehicles. No real chance. Finally, we narrow that road. Still no significant change. And now we're at the situation that would come into being here. So if junctions with 4 rather than 3 arms are considered safe, then this situation should not be considered a safety risk either.

Near where I live in Shoreham-by-Sea, there is a crossroads junction quite similar to that (if you pull up Google Maps, it's where Eastern Avenue joins Middle Road). The north, east and south arms are all normal roads. The west arm is a cul-de-sac to motor vehicles for access to allotments only,  but a through-route for bikes and pedestrians - NCN Route 2 crosses the junction east-west. There are sensor-controlled traffic lights on all arms, and pedestrian crossings are (IIRC) all given green at the same time when requests are put in.

The junction feels very safe but it is worth noting that a large number of cyclists who pass through go through red lights, after checking that it is clear. This is normally worst on the west arm - the lights there are permanently red by default, and I assume many don't expect much to happen. I myself have used the 'scramble' phase because the junction is clear of motor vehicles and the sensors can take a while to kick in.

It's not exactly the same as the proposed cyclepath-opposite-a-cul-de-sac but it shares many similarities, and the most important thing to note here is that safety concerns are minimal and cyclists are at no point expected to dismount, even though the west arm is effectively for cycle use only.

Although I assume the Horsham crossroads will not be signalised, if the main road (not the cycleway or the cul-de-sac) is in a residential area there should be no concerns about fast drivers failing to see cyclists. Perhaps the junction could be treated as a mini-roundabout, giving cyclists concrete priority over the road to their left?

I assume it's the 'crossroads' layout they are worried about (we do not build new four-arm priority junctions). Having said that, it shouldn't be beyond the wit of the council/developer to come up with a design that accommodates cyclists and also gets peds crossing beyond the opposite bellmouth - locating dropped crossings and tactiles in an appropriate location would aid that.

First off - it is a genuine problem. A crossroads is a dangerous junction arrangement that you simply don't see in any modern development - for pretty obvious reasons. The fact that they have spotted the issue with a cycle track shows that at least they are treating the design of the cycle track seriously - though that is as far as I would give them credit for. Discharging the cycle track onto the pavement is pathetic, though sadly typical of highway engineers thinking; they really don't consider us a legitimate road users.

However, there are simple solutions - as others have pointed out - think what would they do if it was a road junction.

The most obvious solution would be to arrange for the cycle track to join the road a few metres to the north or south thus creating a staggered junction.

If the constraints of the site force the junction to be there then you need some form of control to interrupt straight-across movements. A mini-roundabout should be sufficient at such a quiet location.