I'm going to suggest this book for you, also:
http://www.amazon.co.uk/Rodales-Chem.../dp/0878579516

Why? It's not because I'm an organic gardener (I'm not, I garden on the
LISA model, low input sustainable agriculture), but because it has excellent
introductory chapters on soils, on soil fertility, on water and climate, and
on managing weeds, as well as solid information on preparing a site for
flower or vegetable gardens, trees or lawn, and then growing what you want.
If you take the time to read the initial chapters and work through a basic
soil analysis (at least a shake test!) and do the soil preparation and think
through what you want to plant where and why, you'll have a garden that
will look good for many years to come with a whole lot less work and expense
later.

You can't really screw up anything badly with the methods in this book. That's
another reason I like it for people who can only identify a rake 2 out of 3
times. g

What you've done at the moment is set the weeds back a fair bit. But we still
don't know what you've got, or whether it's annual or perennial. Annual
weeds can be controlled pretty easily with pulling or hoeing; perennial weeds
like johnsongrass (unlikely in England!) or yellow nutsedge (Cyperus esculentus)
can spread by underground plant fragments -- pull a yellow nutsedge plant and
you've gotten rid of one plant and started 50 more growing.

The real secret to weed control is to keep the soil covered with plants
you do want -- "canopy closure" in farming terms. If there's bare soil, light
and water, you're going to have weeds.

So here are your choices that I see at this time:

1) Wait till the weeds are growing well and nuke them with a non-specific
herbicide like glyphosate (Roundup). Since you've got a mixed bunch of species,you'll probably have to repeat it several times over the course of months.

2) Use a light occlusive mulch to smother the weeds for several months.
Mow as close as possible, then cover the soil with corrugated cardboard,
old carpet, or 15-30 thicknesses of newspaper or 6" of wood chips. Wait a
few months. Pull the mulch off, add some water and sunlight for a
couple of weeks to get things that survived growing again, and either
dig, re-mulch or nuke with herbicide. (This would be my choice... and I
might consider using a painted-on glyphosate application for certain
very difficult to control weeds, but I don't like wholesale spraying
(commonly known as "spray and pray".) This approach takes several
months to work, bringing you to the fall, which is a good time to plant
cool season grasses like Kentucky bluegrass or most of the fescues.
If you've used cardboard or newspaper, you can till that into the soil.
If you used wool carpet or wood chips, you can compost it and apply it later.

3) Go ahead and till now, raking up all vegetation as it comes up. This is
the hot part of the summer, and a lot of work, but if you need to get
your frustrations out, it might be a viable choice. You'll need to do some
major weed control later, most likely. Plant a cover crop of some sort,
like buckwheat, to help suppress weed growth until you're ready to plant
the entire garden and lawn.

When you've got the weeds under control, chosen the lawn grass you want,
gotten the soil tested and decided how you're going to amend it (if at all),
then you're ready to plant. It's the least work to plant seeds (or sod) when
the conditions are best for that species to grow, and you'll get a lot
fewer weeds poking through the plants you want.

The key to having a nice looking garden or lawn that doesn't drive you nuts
with work and expense is to choose species that will do well under your
conditions. For instance, if you have kids or dogs, you're going to want
a sports-type turfgrass, not something fit for a putting green or a dainty
little moss garden -- you'd be constantly trying to repair the last two.
The more effort you put into it before you plant, the less effort you're going
to need to put into it in the long haul.

In the US, we have an organization in most states called "Master Gardeners",
who are volunteers that are trained in a variety of gardening techniques
and knowledgeable about most common aspects of gardening (and sometimes some
really esoteric stuff, too.) These people are available for consultation on
a variety of gardening problems. You might try to find out if there's a
similar network in the UK. Otherwise, hunt out the best garden centers
you can find and ask for advice and for help identifying your weeds. Or
hire someone knowledgeable on local conditions to help you figure out a plan
of attack that suits both the available energy and cash you can apply to this
set of problems.

Kay