look up john arch henlow bedfordshire

[StevenG]

There was a John ARCH, aged 6, buried in Cardington on 25th May 1848.  It is the only incidence of the surname ARCH in my database (Bedford area only).

(I know this isn't a direct response to the OP, but it may help to fill in some of the detail from Trish's post.)

[bedfordshire boy]

According to a member submission on the IGI, which doesn't show as an extracted item, John Arch who was buried in Cardington was baptised in Cardington on 20 Aug 1843, the son of John Arch and Martha Sims. It needs checking with the parish register to see if it's real, but it might explain the tree that Trish found.

However, if John Arch really was the father of all the children, and he was the only John Arch in Beds at that time, he seems to have flitted between two ladies:
John 1843 mother Martha
John Jackson 1848
Martha Sims 1851 mother Martha
John Sims 1855 mother Martha

[StevenG]

Ah.

Cardington baptisms are up for that period ( http://stevengibbs.me.uk/CardingtonBaptisms-1.htm ) but I couldn't read the father's name on that one.  I'll go back to the register and see if it does say Arch.

[StevenG]

Yes, it does say ARCH - it's much easier when you know what is should be!

It's now corrected.