Hi Bee:
My DD2 (Y4) is somewhat similar. Our solution was to acknowledge that to her it's important to be good at things - to be on top table, to be able to 'keep up' with her peers - even high achieving ones, to be pleasing her violin teacher.... So slowly over the years we've developed a routine which ensures she has lots of practice in areas that matter to her:
More reading - encouraging not just reading to me (10 - 15 minutes while sister bathes) but also reading before bed. Violin practice from 8 - 8:30 a.m. - after she's dressed and getting that practice in with me checking through what she's doing at the weekend (don't play the violin, but piano so can read music and can help with notes/ timing - when I have more time and we can extend the practice if more work is needed).
More writing - she struggled with joined up writing so we bought her workbooks she liked and let her work through them on her own. She now keeps diaries and writes little stories in various notebooks. We just keep supplying them and encourage family/ friends to give her notebooks for birthdays/ Christmas/ etc...
More maths - because DD1 had such problems and was seriously struggling and the school was not intervening - we joined mathsfactor (link: www.themathsfactor.com/) which basically is a video/ video game format to learn calculation skills & practice them. It's hosted by Carol Vorderman (of countdown fame) and is amazingly clear and seems to really appeal to my girls. DD2 asked to do this because she was jealous of DD1 so joined late YR and has done it all the way through. It has meant she's usually known how to do things before it's tackled in class - or has a good idea how to apply the knowledge she has to a new type of problem.
other parents here on MN have recommended:
Mathletics: www.mathletics.co.uk/
Math Whizz: www.whizz.com/
Komodo maths: komodomath.com/
There are also some great free maths websites which offer a lot of practice but may require you to search through to find appropriate games:
woodland junior school maths zone: www.primaryhomeworkhelp.co.uk/maths/
cool maths for kids: www.coolmath-games.com/
Khan Academy (this is a tutorial but free - based on US curriculum so be aware that US grades are one year behind so 5th grade in US = Y6 in UK - basically they start later but move more swiftly): www.khanacademy.org/ - on the black menu bar select LEARN and then select MATH and then select the appropriate year (so -1 from year your DC is currently at).
Basically - it's taken a bit of juggling and reordering of our lives (getting up that 15 minutes earlier) - but we've accommodated DD2s need to be 'on top' of maths/ reading/ writing or violin work and to feel she knows what she needs to do. Because she's well prepared she's lest flustered/ upset in class, she tends to be recognised for her hard work (put on top table, promoted from 3rd to second violins in orchestra, etc...) and so that positive reinforcement feeds back into her recognising that a good routine of practice makes a difference.
The routine makes life more straightforward for DH & I - less surprises/ last minute panics on homework late Sunday p.m. - and the girls are clearly getting good results in school & for DD2 in violin.
I think one reality is that in this area the 11+ is highly competitive - it's free here - state funded - but based on selective exam process. The comprehensive options here are pretty dire on the whole - so many parents start gearing up for the 11+ early (as early as Y3) and have their kids do extra work towards this at home - which means that they start to move ahead of peers not doing as much. The nett result is that kids 'falling behind' feel pressure and confused why X can do it but they can't. It is a choice - but it's also important to acknowledge the personality of your child. For DD1 (who left KS1 with NC L1 across the boards in KS1 SATs) it wasn't an issue - she didn't mind - we minded as parents that she was behind but she was happiest to focus on 'catching up' at a slow but steady pace - not trying to do multiplication with the clever kids, but working on addition/ subtraction to get that, because she knew she couldn't. With DD2 it's always been about being in top group and on level pegging with the most able in the class. She has a very large competitive streak - and we've had to accept that it's her personality and doing more work to keep up/ stay on top is what she needs & wants to do.
HTH